Write out the sum. Do not evaluate.
-$$\sum _ { k = 1 } ^ { n } 2 ^ { k + 1 }$$
A) $2 ^ { 2 } + 2 ^ { 3 } + 2 ^ { 4 } + \ldots + 2 ^ { n + 1 }$
B) $2 + 2 ^ { 2 } + 2 ^ { 3 } + \ldots + 2 ^ { n + 1 }$
C) $2 + 2 ^ { 2 } + 2 ^ { 3 } + \ldots + 2 ^ { n }$
D) $2 ^ { 2 } + 2 ^ { 3 } + 2 ^ { 4 } + \ldots + 2 ^ { n }$

Question

Quizplus · Accepted Answer

The sum starts at $k = 1$ and for each term, it is $2^{k+1}$. So, the first term is $2^{1+1} = 2^2$, and the last term, when $k = n$, is $2^{n+1}$. This matches option A exactly.

Write Out the Sum ∑k=1n2k+1\sum _ { k = 1 } ^ { n } 2 ^ { k + 1 }k=1∑n​2k+1

Write Out the Sum $\sum _ { k = 1 } ^ { n } 2 ^ { k + 1 }$