ช่วย prove หน่อยครับ

[erk12th]

Let $r_n,s_n$ be sequence in $[0,\infty)$ and $\sum_{n = 1}^{\infty} r_n < \infty, \sum_{n = 1}^{\infty} s_n < \infty$ for $\delta_n=\binom{k}{1}r_n+\binom{k}{2}r^2_n+\binom{k}{3}r^3_n+\cdots+\binom{k}{k}r^k_n$ and $c_n=s_n\sum_{i = 1}^k (1+r_n)^{(k-i)}$ prove that $\sum_{n = 1}^{\infty} \delta_n < \infty$ and $\sum_{n = 1}^{\infty} c_n < \infty$.