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Question Number 142646 by naka3546 last updated on 03/Jun/21

$$Provethat$$ $$(1+\frac{1}{2^3})(1+\frac{1}{3^3})(1+\frac{1}{4^3})\dots <3$$

Answered by 1549442205PVT last updated on 04/Jun/21

$$\mathrm{l}.\mathrm{h}.\mathrm{s}=\frac{3(2^2-2+1).4(3^2-3+1).5(4^2-4+1)....}{{(2.3.4...)}^3}$$ $$<\frac{3.2^2.4.3^{2}5.4^2.....}{2^3.{(3.4....)}^3}=\frac{2^2.5.{(3.4....)}^3}{2^3{(3.4...)}^3}=\frac{5}{2}<3$$

Commented bynaka3546 last updated on 04/Jun/21

$$\mathrm{Dank}\mathrm{you},,,\mathrm{thank}\mathrm{you}$$

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