Prove (or disprove) the following statement: For any positive integers $x,y,t$,
$\displaystyle\sum_{i=1}^{t(y+1)-1} \frac{1}{t(xy+x-1)-x+i}$
is an increasing function of $t$.
My attempts: The statement appears to be true numerically. Tried some obvious bounds to compare the sums for consecutive values of $t$ but didn't find one that was strong enough to prove the statement.