(1)+(2+3)+(4+5+6)......n th term, find out the sum of this series upto n th term.
Bikram Saha , 4 Years ago
Grade 11
1 Answers
Aditya Gupta
Last Activity: 4 Years 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 :))
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.