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Question

In the expansion of $open parentheses x plus x to the power of 2 end exponent plus horizontal ellipsis horizontal ellipsis.. close parentheses open parentheses 1 plus x plus x to the power of 2 end exponent plus x to the power of 3 end exponent close parentheses open parentheses x to the power of 2 end exponent plus horizontal ellipsis horizontal ellipsis. plus x to the power of 10 end exponent close parentheses$ the coefficient of is

10
18
30
40

The correct answer is: 10

Related Questions to study

Statement 1:The coefficient of $x to the power of n end exponent$ in the binomial expansion of $left parenthesis 1 minus x right parenthesis to the power of negative 2 end exponent$ is $left parenthesis n plus 1 right parenthesis$
Statement 2:The coefficient of $x to the power of r end exponent$ in $left parenthesis 1 minus x right parenthesis to the power of negative n end exponent$ when $n element of N$ is $blank to the power of n plus r minus 1 end exponent C subscript r end subscript$

Statement 1:The coefficient of $x to the power of n end exponent$ in the binomial expansion of $left parenthesis 1 minus x right parenthesis to the power of negative 2 end exponent$ is $left parenthesis n plus 1 right parenthesis$
Statement 2:The coefficient of $x to the power of r end exponent$ in $left parenthesis 1 minus x right parenthesis to the power of negative n end exponent$ when $n element of N$ is $blank to the power of n plus r minus 1 end exponent C subscript r end subscript$

If the $left parenthesis r plus 1 right parenthesis$ th term in the expansion of $open parentheses fraction numerator a to the power of 1 divided by 3 end exponent over denominator b to the power of 1 divided by 6 end exponent end fraction plus fraction numerator b to the power of 1 divided by 2 end exponent over denominator a to the power of 1 divided by 6 end exponent end fraction close parentheses to the power of 21 end exponent$ has equal exponents of both $a$ and $b$ , then value of $r$ is

If the $left parenthesis r plus 1 right parenthesis$ th term in the expansion of $open parentheses fraction numerator a to the power of 1 divided by 3 end exponent over denominator b to the power of 1 divided by 6 end exponent end fraction plus fraction numerator b to the power of 1 divided by 2 end exponent over denominator a to the power of 1 divided by 6 end exponent end fraction close parentheses to the power of 21 end exponent$ has equal exponents of both $a$ and $b$ , then value of $r$ is

If in the expansion of $left parenthesis 1 plus x right parenthesis to the power of n end exponent$ , the coefficient of $r$ th and $left parenthesis r plus 2 right parenthesis$ th term be equal, then $r$ is equal to

If in the expansion of $left parenthesis 1 plus x right parenthesis to the power of n end exponent$ , the coefficient of $r$ th and $left parenthesis r plus 2 right parenthesis$ th term be equal, then $r$ is equal to

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The sum of the series $not stretchy sum from r equals 0 to n of left parenthesis negative 1 right parenthesis to the power of r end exponent blank to the power of n end exponent C subscript r end subscript open parentheses fraction numerator 1 over denominator 2 to the power of r end exponent end fraction plus fraction numerator 3 to the power of r end exponent over denominator 2 to the power of 2 r end exponent end fraction plus fraction numerator 7 to the power of r end exponent over denominator 2 to the power of 3 r end exponent end fraction plus fraction numerator 15 to the power of r end exponent over denominator 2 to the power of 4 r end exponent end fraction plus... plus m blank t e r m s close parentheses$ is

The sum of the series $not stretchy sum from r equals 0 to n of left parenthesis negative 1 right parenthesis to the power of r end exponent blank to the power of n end exponent C subscript r end subscript open parentheses fraction numerator 1 over denominator 2 to the power of r end exponent end fraction plus fraction numerator 3 to the power of r end exponent over denominator 2 to the power of 2 r end exponent end fraction plus fraction numerator 7 to the power of r end exponent over denominator 2 to the power of 3 r end exponent end fraction plus fraction numerator 15 to the power of r end exponent over denominator 2 to the power of 4 r end exponent end fraction plus... plus m blank t e r m s close parentheses$ is

The coefficient of $t to the power of 24 end exponent$ in the expansion of $open parentheses 1 plus t to the power of 2 end exponent close parentheses to the power of 12 end exponent open parentheses 1 plus t to the power of 12 end exponent close parentheses left parenthesis 1 plus t to the power of 24 end exponent right parenthesis$ is

The coefficient of $t to the power of 24 end exponent$ in the expansion of $open parentheses 1 plus t to the power of 2 end exponent close parentheses to the power of 12 end exponent open parentheses 1 plus t to the power of 12 end exponent close parentheses left parenthesis 1 plus t to the power of 24 end exponent right parenthesis$ is

The coefficient of $x to the power of 5 end exponent$ in the expansion of $open parentheses 1 plus x to the power of 2 end exponent close parentheses to the power of 5 end exponent open parentheses 1 plus x close parentheses to the power of 4 end exponent$ is

The coefficient of $x to the power of 5 end exponent$ in the expansion of $open parentheses 1 plus x to the power of 2 end exponent close parentheses to the power of 5 end exponent open parentheses 1 plus x close parentheses to the power of 4 end exponent$ is

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Let $R equals left parenthesis 2 plus square root of 3 right parenthesis to the power of 2 n end exponent$ and $f equals R minus left square bracket R right square bracket$ where $left square bracket bullet right square bracket$ denotes the greatest integer function, then $R open parentheses 1 minus f close parentheses$ is equal to

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If $left parenthesis 1 plus x plus x to the power of 2 end exponent right parenthesis to the power of n end exponent equals not stretchy sum from r equals 0 to 2 n of a subscript r end subscript x to the power of r end exponent comma blank t h e n blank a subscript 1 end subscript minus 2 a subscript 2 end subscript plus 3 a subscript 3 end subscript horizontal ellipsis minus 2 n a subscript 2 n end subscript$ is equal to

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Let $open square brackets x close square brackets$ denote the greatest integer less than or equal to $x$ . If $x equals open parentheses square root of 3 plus 1 close parentheses to the power of 5 end exponent$ , then $open square brackets x close square brackets$ is equal to

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parallel

$left parenthesis 2 to the power of 3 n end exponent minus 1 right parenthesis$ will be divisible by $left parenthesis for all n element of N right parenthesis$

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Let $C subscript 1 end subscript comma blank C subscript 2 end subscript comma blank C subscript 3 end subscript$ are the usual binomial coefficients. Let $S equals C subscript 1 end subscript plus 2 C subscript 2 end subscript plus 3 C subscript 3 end subscript plus... plus n C subscript n end subscript$ , then $S$ equals

Let $C subscript 1 end subscript comma blank C subscript 2 end subscript comma blank C subscript 3 end subscript$ are the usual binomial coefficients. Let $S equals C subscript 1 end subscript plus 2 C subscript 2 end subscript plus 3 C subscript 3 end subscript plus... plus n C subscript n end subscript$ , then $S$ equals

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The coefficient of $x$ in the expansion of $open parentheses 1 plus x close parentheses open parentheses 1 plus 2 x close parentheses open parentheses 1 plus 3 x close parentheses horizontal ellipsis horizontal ellipsis left parenthesis 1 plus 100 x right parenthesis$ is

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$I f blank open vertical bar x close vertical bar less than fraction numerator 1 over denominator 2 end fraction comma blank t h e n blank t h e blank c o e f f i c i e n t blank o f blank x to the power of r end exponent blank i n blank t h e blank e x p a n s i o n blank o f fraction numerator 1 plus 2 x over denominator left parenthesis 1 minus 2 x right parenthesis to the power of 2 end exponent end fraction comma blank i s$

$I f blank open vertical bar x close vertical bar less than fraction numerator 1 over denominator 2 end fraction comma blank t h e n blank t h e blank c o e f f i c i e n t blank o f blank x to the power of r end exponent blank i n blank t h e blank e x p a n s i o n blank o f fraction numerator 1 plus 2 x over denominator left parenthesis 1 minus 2 x right parenthesis to the power of 2 end exponent end fraction comma blank i s$

In the expansion of $left parenthesis 1 plus x plus x to the power of 2 end exponent plus x to the power of 3 end exponent right parenthesis to the power of 6 end exponent comma$ then coefficient of $x to the power of 14 end exponent$ is

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