Question

For each sequence (an) below and function f, decide whether the sequence (f(an)) converges
and, if it does, find the limit.

an=1/n f(x)=|x+1|

I just dont understand what its asking? i was ill for the lecture and the notes dont seem to be helping

Answer 1

a(n) = 1/n , that is the sequence 1/1, 1/2, 1/3, 1/4, ...

Answer 2

you are asked to determine if

f(1/1) , f(1/2) , f(1/3) , f(1/4) , ... converges

Answer 3

or in other words you are asked whether the sequence
( 1/1 +1 ) , (1/2 + 1) , (1/3 + 1) , ( 1/4 + 1) , ...
converges
note that i left out the absolute value, since all the terms are positive

Answer 4

so what is the limit of ( 1/n + 1) as n->oo
well, 1/n is going to zero, so you have (0 + 1) = 1

Answer 5

alternatively you can show that f( 1/x) -> 1 , so f( 1/n) -> 1

Answer 6

ahhhh yes okay i see that makes sense! thank you