设 $$ex a_0=1,quad a_1=frac{1}{2},quad a_{n+1}=frac{na_n^2}{1+(n+1)a_n} (ngeq 1). eex$$ 试证: $dps{sum_{k=0}^inftyfrac{a_{k+1}}{a_k}}$ 收敛, 并求其值.
设 $$ex a_0=1,quad a_1=frac{1}{2},quad a_{n+1}=frac{na_n^2}{1+(n+1)a_n} (ngeq 1). eex$$ 试证: $dps{sum_{k=0}^inftyfrac{a_{k+1}}{a_k}}$ 收敛, 并求其值.