Find the limits of the sequences \sum_n^\infty=1\frac{n\times\ln(n)}{n^{2}+1} \sum_n^\infty=1\frac{\sin(n)}{n}

bmgf3m

bmgf3m

Answered question

2022-01-07

Find the limits of the sequences
n=1n×ln(n)n2+1
n=1sin(n)n

Answer & Explanation

Laura Worden

Laura Worden

Beginner2022-01-08Added 45 answers

Consider the series
n=1n×ln(n)n2+1
n=1sin(n)n
By applying the Squeeze Theorem, we have
limnsin(n)n=0
limnn×ln(n)n2+1
=limnln(n)n1+1n2
This implies
limnn×ln(n)n2+1
=limnln(n)nlimn1+1n2
=01=0
movingsupplyw1

movingsupplyw1

Beginner2022-01-09Added 30 answers

O, god, thanks

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?