37.10
37.11
37.12
37.13
37.14
37.15
37.16
37.17
37.18
Investigate the series
INFINITE SERIES
313
Hence, the partial sum
The series converges to 1. (The method used here is called "telescoping.")
Study the series
Thus, the series converges to
So
Find the sum of the series 4 — 1+j — & + •••.
This is a geometric series with ratio
and first term a = 4. Hence, it converges to
Test the convergence of
This is a geometric series with ratio r = \ > 1. Hence, it is divergent.
Test the convergence of 3+I + I + I + ---.
The series has the general term
(starting with n = 0), but lim a n = lim
Hence, by Problem 37.1, the series diverges.
Investigate the series
Rewrite the series as
by Problems 37.11
and 37.10.
Test the convergence of
Hence, by Problem 37.1, the series diverges.
Study the series
So the partial sum
Study the series
Thus,
The partial sum