Saturday

August 30, 2014

August 30, 2014

Posted by **sarah** on Thursday, February 21, 2008 at 6:41pm.

1. if the lim as n->infinity of a(sub n)=0, then the sum from n=1 to infinity of a(sub n) converges

i said this was true because I know that if a (sub n) does NOT=0, it diverges

2. if the sum from n=1 to infinity of a(sub n) converges and a(sub n) does not =0, then the sun from n=1 to infinity of 1/(a(sub n)) diverges.

?????

- calculus -
**Count Iblis**, Thursday, February 21, 2008 at 6:53pm1) is false. Counterexample: a_n = 1/n

Try to prove that sum from n=1 to infinity of 1/n is divergent.

"i said this was true because I know that if a (sub n) does NOT=0, it diverges"

Which is logically equivalent to:

Not divergent implies a_n ---> 0.

Of course, a convergent series must be such that a_n --->0. But the reverse is not true. So, the condition a_n ---> 0 is necessary but not sufficient for convergence.

**Related Questions**

CALCULUS-URGENT- no one will respond!!! - we know the series from n=0 to ...

calculus - true of false if the sum of asubn from n=1 to infinity converges, and...

calculus - true of false if the sum of asubn from n=1 to infinity converges, and...

CALCULUS-URGENT - we know the series from n=0 to infinity of c(sub n)*3^n ...

CALCULUS - we know the series from n=0 to infinity of c(sub n)*3^n converges 1...

calculus - 2. if the sum from n=1 to infinity of a(sub n) converges and a(sub n...

calculus - true or false: if the sum from n=1 to infinity of a(n) converges, and...

calculus - true or false- if the sum from n=1 to infinity of a(n) converges and ...

calculus - true or false- if the sum from n=1 to infinity of a(n) converges and ...

Calculus II - Consider the sequence: (a,sub(n))={1/n E(k=1 to n) 1/1+(k/n)} Show...