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Maths-

General

Easy

Question

The sum to n terms of the series $6 times 9 plus 12 times 21 plus 20 times 37 plus 30 times 57 plus 42 times 81 plus midline horizontal ellipsis$ is

$\frac{2}{5} n (n + 1) (n + 2) (n + 3) (n + 4) + \frac{1}{3} (n + 1) (n + 2) (n + 3)$
$\frac{2}{5} n (n + 1) (n + 2) (n + 3) (n + 4) - \frac{1}{3} (n + 1) (n + 2) (n + 3)$
$\frac{2}{5} n (n - 1) (n - 2) (n - 3) (n - 4) + \frac{1}{3} (n - 1) (n - 2) (n - 3)$
None of these

The correct answer is: $fraction numerator 2 over denominator 5 end fraction n left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis n plus 3 right parenthesis left parenthesis n plus 4 right parenthesis plus fraction numerator 1 over denominator 3 end fraction left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis n plus 3 right parenthesis$

$612203042 comma horizontal ellipsis comma n to the power of text th end text end exponent text term end text equals n to the power of 2 end exponent plus 3 n plus 2$
$equals left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis$
$921375781 comma horizontal ellipsis comma n to the power of text th end text end exponent text term end text equals 2 n to the power of 2 end exponent plus 6 n plus 1$
$equals 2 n left parenthesis n plus 3 right parenthesis plus 1$
$text Therefore, end text u subscript n end subscript equals left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left curly bracket 2 n left parenthesis n plus 3 right parenthesis plus 1 right curly bracket$
$equals 2 n left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis n plus 3 right parenthesis plus left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis$
$rightwards double arrow S subscript n end subscript equals fraction numerator 2 over denominator 5 end fraction n left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis n plus 3 right parenthesis left parenthesis n plus 4 right parenthesis plus fraction numerator 1 over denominator 3 end fraction left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis n plus 3 right parenthesis$

Related Questions to study

$text If end text 0 less than alpha less than fraction numerator pi over denominator 2 end fraction text and end text f left parenthesis alpha right parenthesis equals pi to the power of sec to the power of 2 end exponent invisible function application alpha end exponent c o s to the power of 2 end exponent invisible function application alpha plus pi to the power of cosec to the power of 3 end exponent invisible function application alpha end exponent s i n to the power of 2 end exponent invisible function application alpha comma text end text$ then

$text If end text 0 less than alpha less than fraction numerator pi over denominator 2 end fraction text and end text f left parenthesis alpha right parenthesis equals pi to the power of sec to the power of 2 end exponent invisible function application alpha end exponent c o s to the power of 2 end exponent invisible function application alpha plus pi to the power of cosec to the power of 3 end exponent invisible function application alpha end exponent s i n to the power of 2 end exponent invisible function application alpha comma text end text$ then

When Cl₂ is passed into moist slaked like, compound formed is:

When Cl₂ is passed into moist slaked like, compound formed is:

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On igniting Fe₂O₃ at 1400°C, the product obtained is:

On igniting Fe₂O₃ at 1400°C, the product obtained is:

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AgCl on fusion with Na₂CO₃ form

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As the reaction is increased from T₁ to T₂

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The conjugate base of H₃⁺O is

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1 cc of 0.1M HCl is added to 999 cc solution of 0.1M NaCl. The pH of the resulting solution will be

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A gaseous reaction A₂(g) ¾¾→ B(g) + $fraction numerator 1 over denominator 2 end fraction$ C(g) Shows increase in pressure from 100mm to 120 mm in 5 minutes. The rate of disappearance of A₂ is

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For a chemical reaction 2X + Y $⟶$ Z, the rate of appearance of Z is 0.05 mol L^–1 per min. The rate of disappearance of X will be

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An ideal gas expands according to PV = constant. On expansion, the temperature of gas

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The highest excited state that unexcited hydrogen atoms can reach when they are bombarded with 12.2 eV photon is

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The product of the following reaction is

The product of the following reaction is

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