u-n-is-a-arithmetic-sequence-with-u-0-1-and-u-5-11-1-find-the-value-of-S-n-k-0-n-1-u-k-2-and-lim-n-S-n-2-find-the-value-of-W-n-k-1-n-1-u-k-1-u-k

Question Number 35579 by abdo mathsup 649 cc last updated on 20/May/18

$$\left({u}_{{n}} \right)\:{is}\:{a}\:{arithmetic}\:{sequence}\:{with}\:{u}_{\mathrm{0}} =\mathrm{1}\:{and} \\ $$$${u}_{\mathrm{5}} =\mathrm{11}\:\:\:\:\: \\ $$$$\left.\mathrm{1}\right)\:\:{find}\:{the}\:{value}\:{of}\:\:\:{S}_{{n}} \:\:=\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\:\frac{\mathrm{1}}{{u}_{{k}} ^{\mathrm{2}} } \\ $$$${and}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:{W}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{u}_{{k}−\mathrm{1}} .\:{u}_{{k}+\mathrm{1}} } \\ $$$${and}\:{lim}_{{n}\rightarrow+\infty} \:{W}_{{n}} \:. \\ $$

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