Factorial Trouble

Algebra Level 3

$\Large {\displaystyle \sum _{ n=0 }^{ \infty }{ \frac { (2n+1)! }{ [2(n+1)]! } } = \ ? }$

Enter 999 if you think that the series diverges.

The answer is 999.

1 solution

Rishabh Jain
Feb 13, 2016

$\Large \sum_{n=0}^{\infty} \dfrac{\color{#007fff}{(2n+1)!}}{(2n+2)(\color{#007fff}{(2n+1)!})}$ $\Large =\sum_{n=0}^{\infty} \dfrac{1}{2(n+1)}$ which is diverging... Hence answer is $\large\boxed{999}$ .
See this to study the diverging nature of the above series..

... beat me by half of a minute!

Aareyan Manzoor - 5 years, 4 months ago

:-}.... I had to add a link which I did after posting my solution ;-)( Maybe in that span you would have beaten me).

Rishabh Jain - 5 years, 4 months ago

The sum above closely approximates $\ln{n}+\gamma$ .

A Former Brilliant Member - 5 years, 4 months ago

As $n \rightarrow \infty$ , $\ln n + \gamma \rightarrow \infty$

Harsh Shrivastava - 5 years, 4 months ago

Factorial Trouble

The answer is 999.

1 solution

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