Question

1.2.3.4 +2.3.4.5 +3.4.5.6 +............. find Sn of the series
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Answer 1

Answer:

4.5.6.7.

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Answer 2

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$\sf{General\:term \:=n(n+1)(n+2)(n+3)=n⁴+6n³+11n²+6n}$

$\rm{Sum\:of\:n\:terms=∑{n⁴}+6∑n³+11∑n²+6∑n}$

$\sf{=}\dfrac{n^5}{5}+\dfrac{n⁴}{2}+\dfrac{n³}{3}-\dfrac{n}{3}+</p><p>$$\rm{6[}\dfrac{n²(n+1)²}{4}]+$

$\rm{11}\dfrac{[n(n+1)(2n+1)]}{6}+$

$\dfrac{6[n(n+1)]}{2}$

$\mapsto\dfrac{n^5}{5}+2n⁴+7n³+10n²+\dfrac{9n}{2}$

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