Let a_n=sqrt[n](n)-1. Does sum_(n=1^infty) a_n converge?

Hallie Stanton

Hallie Stanton

Answered question

2022-11-08

Let a n = n n 1. Does n = 1 a n converge?

Answer & Explanation

Kristen Garza

Kristen Garza

Beginner2022-11-09Added 13 answers

n n 1 = n 1 n n 1 n + n n 2 n + . . . + 1 n 1 n n n 1 n = n 1 n 1 n n 1 n = n 1 n n n n > n 1 n 1 n
Now use that for all n>2 we have
n 1 n 1 n > 1 2 1 n ,
or limit compare it to the harmonic series.

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