laurely000 laurely000
  • 02-08-2022
  • Mathematics
contestada

S=1 - 1/4 + 1/6 - 1/9 + 1/11 - 1/14..........infinity. Find the sum of series.

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Medunno13
Medunno13 Medunno13
  • 16-08-2022

[tex]1+\frac{1}{6}+\frac{1}{11}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-4} \\ \\ \frac{1}{4}+\frac{1}{9}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-1} \\ \\ S=\sum^{\infty}_{n=1} \left(\frac{1}{5n-4} -\frac{1}{5n-1} \right) \\ \\ =\frac{\pi}{5} \sqrt{\frac{1}{5} (5+2\sqrt{5})}[/tex]

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