compute 10/sigma/t=0 (1/2)^t

Question

compute

10/sigma/t=0 (1/2)^t

Answer 1

∑a_i = a[(1 - rⁿ)/(1 - r), where a = first term, n = number of terms, r = common ratio. 

 

In the given: a = 1, r = 1/2, n = 11

 

∑a_i = 1[1 - (1/2)¹¹]/[1 - (1/2)]

∑ai = 1[1 - (1/2048)]/(-1/2 )

∑ai = 1[ -2047/2048]/(-1/2)

∑ai = 2047/1024

∑ai = 1.99902344