Given-u-n-n-N-suppose-u-2n-n-N-and-u-2n-1-n-N-converge-towards-the-same-limit-L-Show-that-u-n-n-N-equally-converges-to-L-

Question Number 97807 by Ar Brandon last updated on 09/Jun/20

$$\mathcal{G}\mathrm{iven}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} ,\:\mathrm{suppose}\:\left(\mathrm{u}_{\mathrm{2n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{and}\:\left(\mathrm{u}_{\mathrm{2n}+\mathrm{1}} \right)_{\mathrm{n}\in\mathbb{N}} \\ $$$$\mathrm{converge}\:\mathrm{towards}\:\mathrm{the}\:\mathrm{same}\:\mathrm{limit},\:\mathrm{L}. \\ $$$$\mathcal{S}\mathrm{how}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{equally}\:\mathrm{converges}\:\mathrm{to}\:\mathrm{L}. \\ $$

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