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we am working on a mapp to show that the Mann iteration converges. At the end of the computation we came up the series $\sum\alpha_n(k_n(M+1)-1)$, from previous work it is known that the series $\sum\alpha_n(k_n-1)<\infty$.

we wish to know if $\sum\alpha_n(k_n(M+1)-1)<\infty$ and if not why?

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