How do you find the formula for the sum of this?
#sum_(r=1)^(n)2^r#
2 Answers
Explanation:
Subtracting
then adding
switching sides
# sum_(r=1)^n 2^r = 2(2^n-1) #
Explanation:
If we expand the first few terms of the sum we have:
# sum_(r=1)^n 2^r = 2^1+2^2+2^3+ ... + 2^n #
And we notice the terms form a Geometric Progression with first term
#S_n = a(1-r^n)/(1-r) #
We have:
# sum_(r=1)^n 2^r = (2){ (1-2^n)/(1-2)} #
# \ \ \ \ \ \ \ \ \ \ = 2{ (1-2^n)/(-1)} #
# \ \ \ \ \ \ \ \ \ \ = 2(2^n-1) #