# Sum of Reciprocals of Cubes of Odd Integers Alternating in Sign in Pairs

Jump to navigation
Jump to search

## Theorem

\(\displaystyle \frac 1 {1^3} + \frac 1 {3^3} - \frac 1 {5^3} - \frac 1 {7^3} + \cdots\) | \(=\) | \(\displaystyle \frac {3 \pi^3 \sqrt 2} {128}\) |

## Proof

## Sources

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 19$: Series involving Reciprocals of Powers of Positive Integers: $19.29$