Could someone please help me to show whether or not the sum from k=1 to infinity of 1/2k exist or doesn't exist.

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- November 26th 2009, 03:12 AMravenboydoes this sum exist?
Could someone please help me to show whether or not the sum from k=1 to infinity of 1/2k exist or doesn't exist.

- November 26th 2009, 03:21 AMmr fantastic
- November 26th 2009, 03:23 AMKrizalid
it doesn't.

see http://en.wikipedia.org/wiki/Harmoni...s_(mathematics).

(ahh, got beaten.) - November 26th 2009, 03:38 AMravenboy
basically i am trying to prove the sum of k=1 to infinity of 1/(K+ sqrt(k)) doesn't exist.

i know the sequence is greater than or equal to 1/2k and 1/2k doesn't exist so by comparison test our sequence doesn't exist.

how would you show 1/2k doesn't exist? Is it because:

we know 1/k doesn't exist and so 1/2k is just (1/2)*(1/k) so 1/2k doesn't exist.

Am i right in, saying we cant use comparison test to show 1/2k doesnt exist compared to 1/k because (1/2k)<(1/k). thanks for your help thus far. - November 26th 2009, 03:42 AMmr fantastic
- November 26th 2009, 03:45 AMravenboy
thanks. wasn't sure if the following bit

""1/k doesn't exist and so 1/2k is just (1/2)*(1/k) so 1/2k doesn't exist."

was true or not as lecturer didn't really explain that bit, So i was assuming that was true. Thanks again. - November 26th 2009, 06:53 PMredsoxfan325
Any nonzero constant multiple times a sum doesn't change whether it converges or not.