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Find the n^{th} term and sum to n terms of the following serie

Question

Find the $n^{t h}$ term and sum to $n$ terms of the following series:
$2 + 6 + 12 + 20 +$ ____

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Find the

n^{t h}

term and sum to

n

terms of the following series:

2 + 6 + 12 + 20 +

____

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

2 + 6 + 12 + 20 + .........

As we can see that the general term is

r (r + 1)

so, the

n^{t h}

term is

n (n + 1)

Sum of given series upto

n

terms:

\Rightarrow r = 1 \sum n r (r + 1)

= r = 1 \sum n r^{2} + r = 1 \sum n r

= \frac{n ( n + 1 ) ( 2 n + 1 )}{6} + \frac{n ( n + 1 )}{2}

= \frac{n ( n + 1 )}{2} {\frac{2 n + 1}{3} + 1}

= \frac{n ( n + 1 )}{2} \frac{2 n + 4}{3}

= \frac{n ( n + 1 ) ( n + 2 )}{3}

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Question Text	Find the $n^{t h}$ term and sum to $n$ terms of the following series: $2 + 6 + 12 + 20 +$ ____
Answer Type	Text solution:1
Upvotes	150