Chapter 11 - Section 11.1 - Sequences and Summation Notation - Exercise Set - Page 831: 80

False

Let us consider left hand side $\sum_{i=0}^6(-1)^i(i+1)^2$ or, $=(-1)^0(0+1)^2+(-1)^1(1+1)^2+(-1)^2(2+1)^2+(-1)^3(3+1)^2+(-1)^4(4+1)^2+(-1)^5(5+1)^2+(-1)^6(6+1)^2$ or, $=1^2-2^2+3^2-4^2+5^2-6^2+7^2$ This can be summed ups as: or, $=\sum_{j=1}^7(-1)^{(j+1)}j^2$ or, $=-\sum_{j=1}^7(-1)^{j}j^2$ thus, L.H.S $\ne$ R.H.S