Question

use summation notation to express the sum 2 - 1/2 + 1/8 - ... + 1/2048

Answer 1

\[\sum_{n=0}^{6}2/(-4)^n\]

Answer 2

how did u get that ?? can u explain pls.?

Answer 3

see the terms are like 2 which is 2/4^0 then 1/2 which is 2/4 ...1/8 is 2/16 so on

Answer 4

a(1+q+q2+...+q^n-1)=a(1-q^n)/(1-q)
q=-1/4 , n=7 ,a=2 then 2-1/2+1/8...+1/2048=2(1-(-1/4)^7)/(1-(-1/4))
=2(1+1/16348)/(1+1/4)=2*16349*5/(16348*4)=163490/65536=2.49466