\input amstex
3. \; n=k+1 , \; \; \underbrace{a + aq + \cdots + aq^{k-1}}_{a \dfrac{q^k - 1}{q-1}} +  aq^{k} = a \dfrac{q^{k} - 1 + q^{k+1} - q^k}{q-1}   = a \dfrac{q^{k+1} - 1}{q-1}