Proving Convergence Using the Squeeze Theorem: A Brief Guide

[denverhockeyfan]

Homework Statement

Use the squeeze theorem to prove the sequence converges to 0. (Given the lim 1/n=0 and 1/n^2=0.

A) cos n pi / n^2

B) ((-1)^n) ln(n) / n^2

I know you have to show that the sequence "squeezes" between the two given above, but I am having problems doing so, any help would be great. Thanks.

 

[sutupidmath]

Homework Statement

Use the squeeze theorem to prove the sequence converges to 0. (Givin the lim 1/n=0 and 1/n^2=0.

A) cos n pi / n^2

B) ((-1)^n) ln(n) / n^2

Although your notation is a little ambiguous i am assuming that on A) you meant

( cos(npi) )/n^2

remember that
0<=Icos(npi)I<= 1, i am assuming also that n is from naturals, than we can safetly multiply by 1/n^2 (or divide by n^2) because it is also positive, (moreover n^2 is always positive regardless of the sing of n) then we get:

0<=Icos(npi)I/n^2 <= 1/n^2 now taking the limit when n--> infinity what do u get?

Next time show your work, before the people here can give you any help.

B) use the same reasoning here also.