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(1) +(2+3) +(4+5+6) +........... Up to n terms Find the sum

(1) +(2+3) +(4+5+6) +........... Up to n terms
Find the sum

Grade:11

1 Answers

Abhishek Singh
105 Points
2 years ago
Clearly here the nth term of series contains  n natural numbers.
Thus by nth terms total natural numbers will be n(n+1)/2. Now the sum of terms will be 
\begin{align*} S &= \frac{(\frac{n(n+1))}{2})(\frac{n(n+1)}{2}+1)}{2}\\ &= \frac{n(n+1)(n^2+n+3)}{8} \end{align*}

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