Thread: Please check summation of infinite series?

I need to take the sum of (1/k) - (1/(k+4)) as k--> 1 to infinity

My answer is..

-4/(k(k+4))

Is that correct? Please help!!

Nope.
The k is a dummy variable, the final answer is a number, possibly infinity, free of k.

Okay, so I just did some algebraic manipulation before but, that doesn't get to me the answer...then how do it go about it?

Originally Posted by pinkprincess08

Okay, so I just did some algebraic manipulation before but, that doesn't get to me the answer...then how do it go about it?

Write out the terms from k =1 to k = 9, say. What do you notice? What do you think is going to happen in the limt of k --> oo.

Add up the terms that are not going to cancel in the limit.

See attachment only if you haven't figured it out based on Mr fantastic's sage advice.

Sk = 1+(1/2)+(1/3)+(1/4) ?

Originally Posted by Calculus26

See attachment only if you haven't figured it out based on Mr fantastic's sage advice.

TYPO...
you must have meant aged not saged advice.

Originally Posted by matheagle

TYPO...
you must have meant aged not saged advice.

Hardy ha ha. You're a fine one to talk, dad. I have googled you, you know. Only moo is allowed to make jokes about my age (because she's the only member [that I'm aware of] who knows what it is within a bull's roar - well, within a sd, anyway).

Anyhow, since things are getting off-topic and the OP has solved the problem, I'll try and make my old athritic fingers type out Thread Clos

Originally Posted by pinkprincess08

Sk = 1+(1/2)+(1/3)+(1/4) ?

Looks OK (to my aged eyes)