Test the convergence of the following series: n+1−1(n+2)3−1+…+∞

jubateee

jubateee

Answered

2022-01-07

Test the convergence of the following series:
n+11(n+2)31++

Answer & Explanation

limacarp4

limacarp4

Expert

2022-01-08Added 39 answers

Since
n+11(n+2)31=1n521+1n1n(1+2n)31n3
1n52
your method looks fine.
Ethan Sanders

Ethan Sanders

Expert

2022-01-09Added 35 answers

n+11(n+2)31=(n+11)(n+1}+1((n+2)31)(n+1+1)
n((n+2)31)(n+1+1)<nn3
=1n2
Using the p-test, 1n2 converges, and since 0<n((n+2)31)(n+1+1)<1n2, using the comparison test, the original series must also converge.
karton

karton

Expert

2022-01-11Added 439 answers

It is clear that n+11(n+2)311n52 as n. Since the series n=11n2 converges so that the series must be converge

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