Want to test the series 2 − 1 3 3 − 1 + 3 −...

babyagelesszj

babyagelesszj

Answered

2022-06-30

Want to test the series
2 1 3 3 1 + 3 1 4 3 1 + 4 1 5 3 1 +

Answer & Explanation

Ordettyreomqu

Ordettyreomqu

Expert

2022-07-01Added 22 answers

Here, n + 1 1 ( n + 2 ) 3 1 1 n 2 . For n=1, it is true, and then the denominator of given series increases more rapidly than numerator and this rate is greater than the rate in 1 / n 2 , so the given series is bounded by 1 / n 2 and hence 1 n + 1 1 ( n + 2 ) 3 1 ( 1 1 n 2 = π 2 / 6 ). Thus the series converges.

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