What will be summation of n^2 from n=1to n=2n Share with your friends Share 0 Neha Sethi answered this Dear student Your question is not clear and appears to be incomplete. Range of n provided in the question is wrong. So, providing you the similar question so that you can get an idea.find the vaue of ∑k=1nk2Consider the identity (x+1)3-x3=3x2+3x+1Putting x=1,2,3,..,(n-1),n successively,we get23-13=3.12+3.1+133-23=3.22+3.2+143-33=3.32+3.3+1....n3-(n-1)3=3.n-12+3.n-1+1n+13-n3=3.n2+3.n+1adding column wise,we obtainn+13-13=3.12+22+....+n2+3(1+2+3+...+n)+(1+1+1+...+n times)n+13-13=3∑k=1nk2+3∑k=1nk+nn3+3n2+3n=3∑k=1nk2+3n(n+1)2+n ∵∑k=1nk=n(n+1)23∑k=1nk2=n3+3n2+3n-3n(n+1)2-n3∑k=1nk2=2n3+6n2+6n-3n2-3n-2n23∑k=1nk2=2n3+3n2+n23∑k=1nk2=n(n+1)(2n+1)2∑k=1nk2=n(n+1)(2n+1)6 Regards 0 View Full Answer
