Is the $\sum_{i=1}^{k} \frac{1}{k+1-i}$ equal to the Harmonic Series when $\lim_{k\to \infty}$?

Question

It is like starting the summation of the Harmonic Series but from the "end".Could we say that when $\lim_{k\to \infty}$ $\sum_{i=1}^{k} \frac{1}{k+1-i}$ is equal to the Harmonic Series?

Answer 1

$\sum_{i=1}^k\frac1{k+1-i}=\sum_{j=1}^k\frac1j$ for all $k$, therefore your $k$-th term is the $k$-th harmonic number.