If nth term of a series is 1/2 ×n(n+1) then find the sum of n terms of the series ?

1 Answer
Aug 7, 2018

S_n=n/6(n+1)(n+2)Sn=n6(n+1)(n+2)

Explanation:

Here,

n^(th) termnthterm of series is :n/2(n+1)n2(n+1)

So, the sum of first terms of series is:

S_n=1+(1+2)+(1+2+3)+...+n/2(n+1)

:.S_n=sum_(r=1)^n r/2(r+1)=1/2sum_(r=1)^n(r^2+r)

:.S_n=1/2{sum_(r=1)^nr^2+sum_(r=1)^nr}

:.S_n=1/2{n/6(n+1)(2n+1)+n/2(n+1)}

:.S_n=1/2*n/2(n+1){(2n+1)/3+1}

:.S_n=n/4(n+1){(2n+1+3)/3}

:.S_n=n/12(n+1){2n+4}

:.S_n=n/12(n+1)2(n+2)

:.S_n=n/6(n+1)(n+2)