Prove that the limit as p approaches infinity of the summation from k=1 to infinity of 1/k^p =1 and the limit as p approaches 1+ of the summation from k=1 to infinity of 1/k^p= infinity.
Thanks!
Lets call the function...
(1)
First we prove that the limit (1) is if . At this scope we compute the partial sum for of (1) for ...
(2)
... and it is easy to see that is...
(3)
Lets now compute the partial sum for of (1) for ...
(4)
... and it is easy to see that is...
(5)
The results obatined in (3), (4) and (5) allow us to conclude that is...
(6)
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