Consider a function $f: \mathbb{N} ightarrow \mathbb{N} .$ Which of the following guarantees that ${ }^{*} \sum_{i=1}^{n} \frac{1}{i"{2}} \leq 2-f(n)$ for all integers $n geq 1^{*}$ can be proved by induction? (If $(F)$ is true you must select it rather than any other answer. If $(F)$ is false but $(E)$ is true, you must select $(E)$ rather than $(A)$ or (B).) Select one: (A): $f(1)=\frac{1}{2}$ and $f (k+1) \leq f(k)-\frac{1} {(k+1)^{2}}$ for all integers $k \geq 1$ (B): $f(1)=\frac{3}{2}$ and $f(k+1) \leq f(K)-\frac{1} {k^{2}}$ for all integers $k \geq 1$ (C): $f(1)=\frac{1}{2}$ and $f (k+1) \leq f(k)+\frac{1} {(k+1)^{2}}$ for all integers $k \geq 1$ (D): $f(1) =1$ and $f(k+1) \leq f(k)+\frac{1}{k^{2}}$ for all integers $k \geq 1$ (E): both (A) and (B) (F): all of (A), (B), (C) and (D) CS. SD.064