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Prove-that-1-1-2-3-1-1-3-3-1-1-4-3-lt-3-




Question Number 142646 by naka3546 last updated on 03/Jun/21
Prove  that     (1+(1/2^3 ))(1+(1/3^3 ))(1+(1/4^3 )) … < 3
Provethat(1+123)(1+133)(1+143)<3
Answered by 1549442205PVT last updated on 04/Jun/21
l.h.s=((3(2^2 −2+1).4(3^2 −3+1).5(4^2 −4+1)....)/((2.3.4...)^3 ))  <((3.2^2 .4.3^2 5.4^2 .....)/(2^3 .(3.4....)^3 ))=((2^2 .5.(3.4....)^3 )/(2^3 (3.4...)^3 ))=(5/2)<3
l.h.s=3(222+1).4(323+1).5(424+1).(2.3.4)3<3.22.4.325.42..23.(3.4.)3=22.5.(3.4.)323(3.4)3=52<3
Commented by naka3546 last updated on 04/Jun/21
Dank you ,,, thank you
Dankyou,,,thankyou

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