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Question Number 137005 by greg_ed last updated on 28/Mar/21

Hi, guyz !  For R = (1/2)×(3/4)×(5/6)×...×((223)/(224))   and             S = (2/3)×(4/5)×(6/7)×...×((224)/(225)) .  Prove that :  R < (1/(15)) < S.

$$\boldsymbol{\mathrm{Hi}},\:\boldsymbol{\mathrm{guyz}}\:! \\ $$ $$\boldsymbol{\mathrm{For}}\:\boldsymbol{\mathrm{R}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{5}}{\mathrm{6}}×...×\frac{\mathrm{223}}{\mathrm{224}}\:\:\:\boldsymbol{\mathrm{and}}\: \\ $$ $$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{S}}\:=\:\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{4}}{\mathrm{5}}×\frac{\mathrm{6}}{\mathrm{7}}×...×\frac{\mathrm{224}}{\mathrm{225}}\:. \\ $$ $$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\::\:\:\boldsymbol{\mathrm{R}}\:<\:\frac{\mathrm{1}}{\mathrm{15}}\:<\:\boldsymbol{\mathrm{S}}. \\ $$

Commented bygreg_ed last updated on 01/May/21

no answer for this thing ?

$$\mathrm{no}\:\mathrm{answer}\:\mathrm{for}\:\mathrm{this}\:\mathrm{thing}\:?\: \\ $$

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