Question

Problem 1a

Answer 1

Given information

Define an alternating series

Step-by-step explanation

Step 1.

A series with alternating positive and negative terms is known as an alternating series.

Given below an example of alternating series

 

 

% MathType@MTEF@2@1@+=

% feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn

% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr

% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9

% vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x

% fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiabgk

% HiTmaalaaabaGaaGymaaqaaiaaikdaaaGaey4kaSYaaSaaaeaacaaI

% XaaabaGaaG4maaaacqGHsisldaWcaaqaaiaaigdaaeaacaaI0aaaai

% abgUcaRmaalaaabaGaaGymaaqaaiaaiwdaaaGaeyOeI0YaaSaaaeaa

% caaIXaaabaGaaGOnaaaacqGHRaWkcaGGUaGaaiOlaiaac6cacqGH9a

% qpdaaeWbqaaiaacIcacqGHsislcaaIXaGaaiykamaaCaaaleqabaGa

% amOBaiabgkHiTiaaigdaaaGcdaWcaaqaaiaaigdaaeaacaWGUbaaaa

% WcbaGaamOBaiabg2da9iaaigdaaeaacqGHEisPa0GaeyyeIuoaaaa@548C@

\[1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...=\sum\limits_{n=1}^{\infty }{{{(-1)}^{n-1}}\frac{1}{n}}\]