Prove Theorem 7.25 . That is, show that the series sum_{k=1}^{infty} a_{k} and sum_{k=M}^{infty…

Prove Theorem 7.25 . That is, show that the series sum_{k=1}^{infty} a_{k} and sum_{k=M}^{infty} a_{k} either both converge or both diverge. In addition, show that if sum_{k=M}^{infty} a_{k} converges to L, then sum_{k=1}^{infty} a_{k} converges to a_{1}+a_{2}+a_{3}+cdots+a_{M-1}+L .

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