Which of the following sums is larger and by how much? (n=1)
Y1 = 7 over Σ 15/4(pi/10)^n
Y2= 11 over Σ 17/4(4/13)^n
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