Asked by Matias
How I calculate the sum of the series
∞
Σ (1/n^2-4)
n=3
∞
Σ (1/n^2-4)
n=3
Answers
Answered by
oobleck
Note that 1/(n^2-4) = 1/4 [1/(n-2) - 1/(n+2)]
so forget about the factor of 1/4 till the end.
Now look at the series.
1/1 - 1/5 + 1/2 - 1/6 + 1/3 - 1/7 + 1/4 - 1/8 + 1/5 - 1/9 + ...
Notice that all of the fractions from 1/5 on up disappear, leaving
1/1 + 1/2 + 1/3 + 1/4 = 25/12
Finally, 1/4 * 25/12 = 25/48
so forget about the factor of 1/4 till the end.
Now look at the series.
1/1 - 1/5 + 1/2 - 1/6 + 1/3 - 1/7 + 1/4 - 1/8 + 1/5 - 1/9 + ...
Notice that all of the fractions from 1/5 on up disappear, leaving
1/1 + 1/2 + 1/3 + 1/4 = 25/12
Finally, 1/4 * 25/12 = 25/48
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.