I have this expression that is being simplified but I don't understand this part:
$2^{k+1} - \sum^k_{i=0}2^i = 2^{k+1} - \sum^{k-1}_{i=0}2^i-2^k = 2^{k} - \sum^{k-1}_{i=0}2^i$
how is $2^{k+1}$ turned into $2^{k}$ when $-2^k$ is removed?
How is this mathemathical "shortcut" made (dumb question)
-1
$\begingroup$
arithmetic
-
2$2^{k+1}=2\times 2^k$ – 2017-02-23
-
0$2^{k+1}=2(2^k)$. $2(2^k)-2^k=2^k$. – 2017-02-23
1 Answers
3
$2^{k+1}-2^k = 2^k (2-1)=2^k$.