# Compute the sum k=1 100000 1/k and sum k=1 1000000 1/k. Are there any differences? Compute the sum k=1 100000 1/k^2 and sum k=1 1000000 1/k^2. Are there any differences?

Mauricio Mathis 2022-07-27 Answered
Compute the sum $\sum _{k=1}^{10000}\frac{1}{k}$ and $\sum _{k=1}^{100000}\frac{1}{k}$. Are there any differences?
Compute the sum $\sum _{k=1}^{100000}\frac{1}{{k}^{2}}$ and $\sum _{k=1}^{1000000}\frac{1}{{k}^{2}}$. Are there any differences?
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Jaylene Tyler
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

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