Thread: easy series question

I just have some basic questions about series in calculus:

is the Infinite Series always positive and getting smaller for it to converge?

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my other question is:

is the telescoping series and collapsing series the same exact series?

thanks.

Originally Posted by rcmango

I just have some basic questions about series in calculus:

is the Infinite Series always positive and getting smaller for it to converge?

No.

is the telescoping series and collapsing series the same exact series?

thanks.

Yes.

Originally Posted by rcmango
I just have some basic questions about series in calculus:

is the Infinite Series always positive and getting smaller for it to converge?


No.

Okay, is an infinite series monotonic? Can an infinite series be bounded?

thanks

Originally Posted by rcmango

Okay, is an infinite series monotonic? Can an infinite series be bounded?

thanks

Let s_n = 1

Then,

SUM (s_n) = +oo
It is not bounded.

And it does not need to be monotonmic.
Let,
t_n=(-1)^n
Then,
SUM (t_n) changes between -1 and +1 it cannot be monotomic.