Use Exercise 89 to determine how many terms of each series are needed so that the partial sum is within 10^-6 of the value of the series that is, to ensure |R_n| -6).

a.

b.

Data from Exercise 89

Consider the geometric series which has the value 1/(1 - r) provided |r| be the sum of the first n terms. The magnitude of the remainder R_n is the error in approximating S by S_n. Show that?

Transcribed Image Text:

E k=0 TT k Ë k=0 e k S = pk k=0 R₁ = S-S₁ Sn ph 1 – r