All Questions Topic List
Others Questions
Previous in All Question Next in All Question
Previous in Others Next in Others
Question Number 111466 by Dwaipayan Shikari last updated on 03/Sep/20
∑∞n=1nnn!
Commented by Her_Majesty last updated on 03/Sep/20
forlargen:n!≈nne−n2πn⇒nnn!≈en2πnlimn→∞en2πn=∞⇒∑∞n=1nnn!=∞
...but∑∞n=1n!nnexists
Answered by malwaan last updated on 03/Sep/20
limn→∞(an+1an)=limn→∞((n+1)n+1(n+1)!×n!nn)=limn→∞(n+1)n(n+1)n!(n+1)n!nn=limn→∞(n+1n)n=limn→∞(1+1n)n=e>1⇒Σ∞n=1nnn!=∞(divergent)
Terms of Service
Privacy Policy
Contact: info@tinkutara.com