Math, asked by chandanasnehal, 1 year ago

what is sigma 2^n. i need the answer by 1 pm ,please send it soon.............

rational: hey are you looking for partial sum of 2^n ?

chandanasnehal: yes

rational: what about the index ? is it starting from 0 or 1 ?

chandanasnehal: nth term is 2^n + n^1, then sum of n terms is, sigma 2^n + n^1

chandanasnehal: how to solve this

chandanasnehal: i am waiting...........................

rational: could you please take a screenshot of actual complete question and attach

chandanasnehal: ok

chandanasnehal: i have a problem with my camera

rational: Ohk.. see if the answer makes sense

Answers

Answered by rational

$\sum\limits_{n=0}^N2^n~~=~~2^0+2^1+2^2+\cdots+2^N$

This is a geometric series with common ratio = $2$ and it has $N+1$ terms.
Using partial sum formula, the sum equals :
$=\frac{2^{N+1}-1}{2-1}$

$=2^{N+1}-1$

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