calculate-n-1-1-n-n-1-n-3- Tinku Tara June 3, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 74887 by abdomathmax last updated on 03/Dec/19 calculate∑n=1∞(−1)n(n+1)n3 Commented by mathmax by abdo last updated on 21/Dec/19 letdecomposeF(x)=1(x+1)x3⇒F(x)=ax+bx2+cx3+dx+1c=x3F(x)∣x=0=1d=(x+1)F(x)∣x=−1=−1⇒F(x)=ax+bx2+1x3−1x+1limx→+∞xF(x)=0=a−1⇒a=1⇒F(x)=1x+bx2+1x3−1x+1F(1)=12=1+b+1−12⇒b+2=1⇒b=−1⇒F(x)=1x−1x2+1x3−1x+1⇒∑n=1∞(−1)n(n+1)n3=∑n=1∞(−1)nn−∑n=1∞(−1)nn2+∑n=1∞(−1)nn3−∑n=1∞(−1)nn+1wehave∑n=1∞(−1)nn=−ln(2)∑n=1∞(−1)nn2=(21−2−1)ξ(2)=−12×π26=−π212∑n=1∞(−1)nn3=(21−3−1)ξ(3)=(14−1)ξ(3)=−34ξ(3)∑n=1∞(−1)nn+1=∑n=2∞(−1)n−1n=∑n=1∞(−1)n−1n−1=ln(2)−1⇒S=−ln(2)+π212−34ξ(3)−ln(2)+1=1−2ln(2)+π212−34ξ(3) Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: We-know-that-R-Q-Q-C-Is-there-another-set-V-such-that-C-V-Next Next post: calculate-x-1-x-3-x-2-2-dx- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.