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A series obtained from a given series by suppression of some of its terms converges,then the given series itself converges and vice versa. $$S_n= C_k + \Delta_{n-k}$$ $S_n=$ sum of first n terms

$C_k=$sum of k 'finite' suppressed terms.

My question is-Is it possible to have $C_k$ as infinite.

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  • $\begingroup$ Please include your own thoughts and the effort made thus far, so that people can work with you accordingly. Please add those in the body of the question instead of commenting. $\endgroup$ – Lee David Chung Lin 2 days ago
  • $\begingroup$ If the original series converges absolutely, you can remove or suppress as many terms as you like. If the original series converges only conditionally, then anything is possible if you remove an infinite number of terms. $\endgroup$ – Xander Henderson 2 days ago