Question
Give an example where $\sum_{k=1}^{\infty} a_{k}$ and $\sum_{k=1}^{\infty} b_{k}$ both diverge but $\sum_{k=1}^{\infty}\left(a_{k}+b_{k}\right)$ converges.
Step 1
This is a harmonic series and it is well known that the harmonic series diverges. Show more…
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