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Question Number 157891 by HongKing last updated on 29/Oct/21

Answered by TheSupreme last updated on 29/Oct/21

$$(\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+\frac{9}{400}+\frac{11}{900})x<70$$$$\left(\frac{2400+500+175+81+44}{3600}\right)x<70$$$$\left(\frac{8}{9}\right)x<70$$$$x<\frac{630}{8}=78.75$$$$largestx=78$$$$$$$$$$

Commented by HongKing last updated on 29/Oct/21

$$\mathrm{a})74\mathrm{b})71\mathrm{c})69\mathrm{d})64\mathrm{e})55$$

Answered by mr W last updated on 29/Oct/21

$$\frac{2k+1}{k^2{(k+1)}^2}=\frac{1}{k^2}-\frac{1}{{(k+1)}^2}$$$$\mathrm{\Sigma }=(\frac{1}{1^2}-\frac{1}{2^2})+(\frac{1}{2^2}-\frac{1}{3^2})+...+(\frac{1}{5^2}-\frac{1}{6^2})$$$$=\frac{1}{1^2}-\frac{1}{6^2}=1-\frac{1}{36}=\frac{35}{36}$$$$\frac{35}{36}x<70$$$$x<\frac{70\times 36}{35}=72$$$$\Rightarrow x_{max}=71\Rightarrow answerb$$

Commented by HongKing last updated on 29/Oct/21

$$\mathrm{alot}\mathrm{thankyou}\mathrm{ser}\mathrm{cool}$$

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