Chapter 5: Integrals - Section 5.2 - Sigma Notation and Limits of Finite Sums - Exercises 5.2 - Page 265: 7

All of them represent 1 +2 +4 +8 +16 +32

(a)6$\Sigma k=1 $ =$2^{1-1}$ +$2^{2-1}$ +$2^{3-1}$+ $2^{4-1}$+ $2^{5-1}$+$2^{6-1}$ =1+ 2+ 4+ 8 +16+ 32 (b) 5$\Sigma k=0 $ =$2^{0}$ +$2^{1}$ +$2^{2}$+ $2^{3}$+ $2^{4}$+$2^{5}$ =1+ 2+ 4+ 8 +16+ 32 (c) 4$\Sigma k=1 $ =$2^{-1+1}$ +$2^{0+1}$ +$2^{1+1}$+ $2^{2+1}$+ $2^{3+1}$+$2^{4+1}$ =1+ 2+ 4+ 8 +16+ 32 All of them represent 1 +2 +4 +8 +16 +32