sum n=1 oo n^n / (n)! a_n+1 / a_n = edit: looked funny when i typed it in... (n+1)^(n+1) / (n+1)! times n! / n^n = [n^n(n+1)^n(n+1)] / n+1 = n^n(n+1)^n did i do the algebra right? what do i do next? ><
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Originally Posted by jeph sum n=1 oo n^n / (n)! Ratio test. (n+1)^(n+1)/(n+1)! * n!/n^n (n+1)^(n+1)/[(n+1)*n!] * n!/n^n (n+1)^n/n^n [(n+1)/n]^n [1+1/n]^n The limit is e>1 Thus it does not converge.
Originally Posted by ThePerfectHacker Ratio test. [(n+1)/n]^n [1+1/n]^n The limit is e>1 Thus it does not converge. how did you turn the first n to a 1 in the first part? how did you get e? i dont get it...
Originally Posted by jeph how did you turn the first n to a 1 in the first part? how did you get e? i dont get it... (n+1)/n = (n/n)+(1/n)=1+1/n Now the limit you need to memorize is that, (1+1/n)^n ---> e
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