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Category: Relation and Functions

1-calculate-n-0-x-n-4n-2-1-with-x-lt-1-2-find-the-value-of-n-0-1-4n-2-1-and-n-0-1-n-4n-2-1-

Question Number 94331 by mathmax by abdo last updated on 18/May/20 $$\left.\mathrm{1}\right)\:{calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{x}^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}…

Given-f-xy-f-x-y-and-f-7-7-find-f-1008-

Question Number 94318 by john santu last updated on 18/May/20 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{xy}\right)\:=\:\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\:\mathrm{and}\: \\ $$$$\mathrm{f}\left(\mathrm{7}\right)\:=\:\mathrm{7}.\:\mathrm{find}\:\mathrm{f}\left(\mathrm{1008}\right)\: \\ $$ Commented by Rasheed.Sindhi last updated on 18/May/20 $${f}\left(\mathrm{7}\right)={f}\left(\mathrm{7}×\mathrm{1}\right)={f}\left(\mathrm{7}+\mathrm{1}\right)=\mathrm{7} \\ $$$${f}\left(\mathrm{8}\right)=\mathrm{7}…

study-the-convergence-of-u-n-k-0-n-1-1-k-2-argsh-n-and-v-n-k-0-n-1-1-k-2-

Question Number 28538 by abdo imad last updated on 26/Jan/18 $${study}\:{the}\:{convergence}\:{of} \\ $$$${u}_{{n}\:} \:\:=\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{k}^{\mathrm{2}} }}\:\:−{argsh}\left({n}\right)\:\:{and} \\ $$$${v}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{k}^{\mathrm{2}} }}\:\:. \\ $$$$…

prove-that-n-N-1-1-n-1-2-argsh-n-1-argsh-n-1-1-n-2-

Question Number 28537 by abdo imad last updated on 26/Jan/18 $${prove}\:{that}\:\:\:\forall\:{n}\in\:\mathbb{N} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\left({n}+\mathrm{1}\right)^{\mathrm{2}} }}\:\leqslant\:{argsh}\left({n}+\mathrm{1}\right)\:−{argsh}\left({n}\right)\leqslant\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{n}^{\mathrm{2}} }}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com