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.
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.