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Scilla [17]
2 years ago
5

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

Mathematics
1 answer:
Ann [662]2 years ago
5 0

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})}

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