Compute the sum Sigmak 110000 1k and Sigmak 1100000 1k Are

Compute the sum Sigma_k = 1^10000 1/k and Sigma_k = 1^100000 1/k. Are there any differences? Compute the sum Sigma_k = 1^10000 1/k^2 and Sigma_k = 1^100000 1/k^2. Are there any difference?

Solution

We are taking k = 1 to 10000 for the first one and k = 1 to 100000 for the second one.

So, yes, definitely, for the first one, we have :

1/1 + 1/2 + 1/3 + .... 1/10000

Second one would be 1/1 + 1/2 + 1/3 + .... 1/10000 + 1/10001 + 1/10002 + .... 1/99999 + 1/100000

So, yes, the second one would be slightly larger but yes, they will be different