calculate-U-n-k-1-n-k-k-1-

Question Number 73034 by mathmax by abdo last updated on 05/Nov/19

c a l c u l a t e U_{n} = \sum_{k = 1}^{n} \frac{k}{(k + 1)!}

Commented by mathmax by abdo last updated on 06/Nov/19

w e h a v e U_{n} = \sum_{k = 1}^{n} \frac{k + 1 - 1}{(k + 1)!} = \sum_{k = 1}^{n} (\frac{1}{k!} - \frac{1}{(k + 1)!})

= 1 - \frac{1}{2!} + \frac{1}{2!} - \frac{1}{3!} + \dots . + \frac{1}{n!} - \frac{1}{(n + 1)!} = 1 - \frac{1}{(n + 1)!}

Answered by mind is power last updated on 05/Nov/19

Un = \underset{k = 1}{\sum^{n}} \frac{1}{k!} - \frac{1}{(k + 1)!} = 1 - \frac{1}{(n + 1)!}