Testing for convergence
Sum of n^2/n! starting at n=1 & to infinity and also Sum of n!/(n^n) starting at n=1 & to infinity.thanks for your help
Sum of n^2/n! starting at n=1 & to infinity and also Sum of n!/(n^n) starting at n=1 & to infinity.thanks for your help
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Do the ratio test.
|a_(n+1) / a_n |
[(n + 1)^2 / (n + 1)!] / [n^2 / n!]
= [(n + 1)^2 / (n + 1)!] * [n! / n^2]
= [(2n + 1) / (n + 1)]
= 2 --> it converges...but 2 is not necessarily the actual number that it converges to.
|a_(n+1) / a_n |
[(n + 1)^2 / (n + 1)!] / [n^2 / n!]
= [(n + 1)^2 / (n + 1)!] * [n! / n^2]
= [(2n + 1) / (n + 1)]
= 2 --> it converges...but 2 is not necessarily the actual number that it converges to.