Thread: convergence of 1/n as a sequence, but not as a series, why?

The sequence, 1/n converges to 0 right, because the limit as n-? is 0.

So why does the series of 1/n diverge? Doesn't The sequence's convergence imply that at some point, the series will simply be adding 0's to a finite number?

Originally Posted by StudentMCCS

The sequence, 1/n converges to 0 right, because the limit as n-? is 0.
So why does the series of 1/n diverge? Doesn't The sequence's convergence imply that at some point, the series will simply be adding 0's to a finite number?

Define the nth partial sum to be .

Now with induction it is easy to show that

Thus