Question
Use mathematical induction to prove each of the following$\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\cdots+\frac{1}{n(n+1)}=\frac{n}{n+1}$
Step 1
For $n=1$, the left-hand side (LHS) of the equation is $\frac{1}{1 \cdot 2} = \frac{1}{2}$ and the right-hand side (RHS) is $\frac{1}{1+1} = \frac{1}{2}$. Since LHS = RHS, the statement holds for $n=1$. Show more…
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