How to calculate the sum of a general series like..
Sum of n(n+2) from n=1 to n=30??
Sum of n(n+2) from n=1 to n=30??
-
The sum of n terms is simplified by induction to be n(n+1)/2. Likewise, the sum of n^2 is simplified to n(1+n)(1+2n)/6, so we have in our sum
sum(n*(n+2), n=1..N) = sum(n^2+2*n, n=1..N) = sum(n^2, n=1..N)+2*sum(n,n=1..N)
= N(1+N)(1+2N)/6 + 2(N(N+1))/2
which if we plug in N=30, we obtain the value 10,385
sum(n*(n+2), n=1..N) = sum(n^2+2*n, n=1..N) = sum(n^2, n=1..N)+2*sum(n,n=1..N)
= N(1+N)(1+2N)/6 + 2(N(N+1))/2
which if we plug in N=30, we obtain the value 10,385