Mathematical Methods in the Physical Sciences · Problem 7.9
INFINITE SERIES, POWER SERIES — Mary Boas
Mathematics — Methods · absolute-convergence
Problem
Prove that an absolutely convergent series n=1∑∞an is convergent. Hint: Put bn=an+∣an∣. Then the bn are nonnegative; we have ∣bn∣≤2∣an∣ and an=bn−∣an∣.