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(1)+(2+3)+(4+5+6)......n th term, find out the sum of this series upto n th term.

(1)+(2+3)+(4+5+6)......n th  term, find out the sum of this series upto n th term.

Grade:11

1 Answers

Aditya Gupta
2075 Points
11 months ago
Note that the last number in the bracket of each term (1,3,6,...) is simply the set of triangular numbers. So, in nth bracket, the last term would be n(n+1)/2 [nth triangular number].
Now, the sum of the given series is clearly equal to S= 1+2+3+.....+m where m is the last term of the nth bracket.
So S= m(m+1)/2 (sum of natural numbers)
But m= n(n+1)/2
So substitute this value of m in S to get
S= n(n+1)(n^2+n+2)/8
KINDLY APPROVE :))

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