Given information
Given series
Step-by-step explanation
Step 1.
Observe that the given series is an alternating series, so
Write in summation form as
% MathType@MTEF@2@1@+=
% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
% vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
% fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyamaaBa
% aaleaacaWGUbaabeaakiabg2da9iabg2da9iaaisdacaGGOaGaeyOe
% I0IaaGymaiaacMcadaahaaWcbeqaaiaad6gacqGHRaWkcaaIXaaaaO
% GaeyyXIC9aaSaaaeaacaaIXaaabaGaamOBaiabgUcaRiaaiAdaaaaa
% aa@463F@
${{a}_{n}}==4{{(-1)}^{n+1}}\cdot \frac{1}{n+6}$