I'm having a lot of trouble with this induction problem. We have a sequence of numbers defined by $X_i = \sum_{j=1}^i \frac{1}{j}$. The objective is, if we have an integer $i>1$, to show that $\sum_{j=1}^{i-1} X_j = iX_i - i$
induction with sequences
0
$\begingroup$
sequences-and-series
induction
-
0So far I have, by induction, that $\sum_{j=1}^{i} X_j = iX_i - i$. Then I have $\sum_{j=1}^{i} X_j=\sum_{j=1}^{i-1} X_j +\sum_{j=i}^{i} X_j$, where the first term uses the inductive assumption. But after this, I've hit a wall – 2011-10-12