I want to determine the limit of the following sequence x n </msub> =

NastreteMutvh5j0

NastreteMutvh5j0

Answered question

2022-06-04

I want to determine the limit of the following sequence
x n = 2 1 + 3 2 2 + 4 3 3 2 + . . . + ( n + 1 ) n n n 1 n 2

Answer & Explanation

tabustudiofx52n

tabustudiofx52n

Beginner2022-06-05Added 6 answers

After applying Stolz-Cesàro we get
lim n k = 1 n ( k + 1 ) k k k 1 n 2 = lim n ( n + 1 ) n n n 1 n 2 ( n 1 ) 2 = lim n ( n + 1 n ) n 2 1 / n = e / 2
Mary Ashley

Mary Ashley

Beginner2022-06-06Added 3 answers

we have :
( n + 1 ) n n n 1 = n n n n 1 ( 1 + 1 n ) n = n ( 1 + 1 n ) n n e
then :
k = 1 n ( k + 1 ) k k k 1 k = 1 n k e = e n ( n + 1 ) 2
So ;
k = 1 n ( n + 1 ) n n n 1 n 2 e n ( n + 1 ) 2 n 2 e 2

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?