Question

which of the following sums is larger and by how much?
1. 7 over Sigma 15/4(pi/10)^n

2. 11 over Sigma 17/4(4/13)^n

please help me with the steps on how to figure this out! thanks

Answer 1

did you mean
Σ ((15/4) (π/10)^n , where n goes from 1 to 7 ?

of so, then you would have

(15/4) [ π/10 + π^2/100 + ... + π^7/10^7)
the [..] is a geometric series where a=π/10 and r = π/10 for 7 terms

the value of the [..]
= (π/10)((π/10)^7 - 1)/(π/10 - 1) = appr. .4579
so
Σ ((15/4) (π/10)^n , where n goes from 1 to 7
= (15/4)(.4579) = 1.717

evaluate the second part the same way, and compare sums

Answer 2

I believe the answer was IF so not OF so, thank you.