Heptagonal Number - Sum of Reciprocals

Sum of Reciprocals

A formula for the sum of the reciprocals of the heptagonal numbers is given by:

\sum_{n=1}^\infty \frac{2}{n(5n-3)} = \frac{1}{15}{\pi}{\sqrt{25-10\sqrt{5}}}+\frac{2}{3}\ln(5)+\frac{{1}+\sqrt{5}}{3}\ln\left(\frac{1}{2}\sqrt{10-2\sqrt{5}}\right)+\frac{{1}-\sqrt{5}}{3}\ln\left(\frac{1}{2}\sqrt{10+2\sqrt{5}}\right)

Read more about this topic:  Heptagonal Number

Famous quotes containing the words sum of and/or sum:

    “To help, to continually help and share, that is the sum of all knowledge; that is the meaning of art.”
    —Eleonora Duse (1859–1924)

    “Genius is no more than childhood recaptured at will, childhood equipped now with man’s physical means to express itself, and with the analytical mind that enables it to bring order into the sum of experience, involuntarily amassed.”
    —Charles Baudelaire (1821–1867)