A series goes 1 + 1/2 + 2/3 + 3/4 + 4/5....
Is there a possible summation equation for this series?
Since it gets smaller only after the first term and never anywhere else.
Answer
Since the general term is larger than $\frac12$, the sum is larger than $\frac12\times$ the number of terms and hence it diverges.
The partial sum is related to the Harmonic numbers.
$$1 + \frac12 + \frac23 + \frac34 + \frac45...=1+\sum_{k=1}^n\frac{k-1}k=1+\sum_{k=1}^n(1-\frac1k)=1+n-H_n.$$
The Harmonic numbers only grow as the logarithm of $n$.
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