Sum of divergent infinite series

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 $n$.