Limiting sigma

Calculus Level 3

$\large \sum_{r=1}^\infty \dfrac r{1\times3\times5\times7\times\cdots\times(2r+1)} = \ ?$

\frac {1}{3}

\frac {2}{3}

\frac {2}{5}

\frac {1}{2}

1 solution

Otto Bretscher
Oct 12, 2015

One can easily show, by induction, that the partial sum up to $r$ is $\frac{1}{2}-\frac{1}{2(1*3*5*....*(2r+1))}$ . This sum goes to $\boxed{\frac{1}{2}}$ as $r\rightarrow\infty$ .

Limiting sigma

1 solution

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