(Solved): hi please answer these thanks.  (d) Is it necessarily true that if \( t_{1}, t_{2}, t_{3}, \ldo ...

(d) Is it necessarily true that if \( t_{1}, t_{2}, t_{3}, \ldots \) are positive and \( \sum_{n=1} t_{n} \) converges, then \( \sum_{n=1} t_{n}^{4} \) also converges? Either prove that it is true or find a counterexample to prove that it is false. [2 marks] (e) What if we remove the restriction that the terms be positive from the previous question? That is, suppose that if \( t_{1}, t_{2}, t_{3} \ldots \) are real numbers and \( \sum_{n=1}^{\infty} t_{n} \) converges, then is it always the case that \( \sum_{n=1}^{\infty} t_{n}^{4} \) also converges? Either prove that it is true or find a counterexample to prove that it is false. [2 marks]