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Maths-

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Question

Find the sum $open parentheses x plus 2 close parentheses to the power of n minus 1 end exponent plus open parentheses x plus 2 close parentheses to the power of n minus 2 end exponent open parentheses x plus 1 close parentheses plus open parentheses x plus 2 close parentheses to the power of n minus 3 end exponent open parentheses x plus 1 close parentheses to the power of 2 end exponent plus horizontal ellipsis plus open parentheses x plus 1 close parentheses to the power of n minus 1 end exponent$

${(x + 2)}^{n - 2} - {(x + 1)}^{n}$
${(x + 2)}^{n - 1} - {(x + 1)}^{n - 1}$
${(x + 2)}^{n} - {(x + 1)}^{n}$
None of these

The correct answer is: $open parentheses x plus 2 close parentheses to the power of n end exponent minus open parentheses x plus 1 close parentheses to the power of n end exponent$

We have,
$fraction numerator open parentheses x plus 2 close parentheses to the power of n end exponent minus open parentheses x plus 1 close parentheses to the power of n end exponent over denominator open parentheses x plus 2 close parentheses minus open parentheses x plus 1 close parentheses end fraction$
$equals open parentheses x plus 2 close parentheses to the power of n minus 1 end exponent plus open parentheses x plus 2 close parentheses to the power of n minus 2 end exponent open parentheses x plus 1 close parentheses plus open parentheses x plus 2 close parentheses to the power of n minus 3 end exponent open parentheses x plus 1 close parentheses to the power of 2 end exponent plus horizontal ellipsis open parentheses x minus 1 close parentheses to the power of n minus 1 end exponent$
Hence, the required sum is
$open parentheses x plus 2 close parentheses to the power of n end exponent minus open parentheses x plus 1 close parentheses to the power of n end exponent blank left square bracket because blank open parentheses x plus 2 close parentheses minus open parentheses x plus 1 close parentheses equals 1 right square bracket$

Related Questions to study

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Set builder form of the relation
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Set builder form of the relation
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parallel

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