Compute the sum ∑ k = 1 10000 1 k and ∑ k = 1 100000 1 k . Are there any differences?Compute the sum ∑ k = 1 100000 1 k 2 and ∑ k = 1 1000000 1 k 2 . Are there any differences?

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Compute the sum       ∑          k      =      1              10000            1    k   and       ∑          k      =      1              100000            1    k  . Are there any differences?Compute the sum       ∑          k      =      1              100000            1          k      2       and       ∑          k      =      1              1000000            1          k      2      . Are there any differences?

Jaylene Tyler · Accepted Answer

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 + .... 1/10000Second one would be 1/1 + 1/2 + 1/3 + .... 1/10000 + 1/10001 + 1/10002 + .... 1/99999 + 1/100000So, yes, the second one would be slightly larger but yes, they will be different

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?

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