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Question Number 155478 by alcohol last updated on 01/Oct/21

Π_(k = 1 ) ^n (1 + (1/k))^k = V_n find V_n

∏nk=1(1+1k)k=VnfindVn

Answered by mindispower last updated on 01/Oct/21

=Π_(k=1) ^n (((k+1)^k )/k^k )=Π(((k+1)^(k+1) )/(k^k .(1+k))) =(((1+n)^(n+1) )/(.(n+1)!))=(((1+n)^n )/(n!))

=∏nk=1(k+1)kkk=Π(k+1)k+1kk.(1+k)=(1+n)n+1.(n+1)!=(1+n)nn!

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