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Finding the Infinite Sum of a Series?
Given the series below (not geometric), find the infinite sum of the series.
1/(1*3) + 1/(3*5) + 1/(5*7) . . .
Since this series is not geometric or arithmetic, what is the proper approach? Slightly confused on how to start...
Any help is greatly appreciated thank you
2 Answers
- 7 years ago
A / (2n + 1) + B / (2n + 3) = (0n + 1) / ((2n + 1) * (2n + 3))
A * (2n + 3) + B * (2n + 1) = 0n + 1
2An + 2Bn = 0n
A + B = 0
B = -A
3A + B = 1
3A - A = 1
2A = 1
A = 1/2
B = -1/2
(1/2) / (2n + 1) - (1/2) / (2n + 3) =>
(1/2) * (1/(2n + 1) - 1/(2n + 3))
Expand the series
(1/2) * (1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ....
(1/2) * 1
1/2
- ted sLv 77 years ago
HINT : you have Σ { n - 0,,2,...} [ 1 / (2n+1)(2n+3) ]...remember the concept of PARTIAL fractions ?
