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Lê Anh Duy

21/03/2018 at 15:11
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THE QUESTIONS TODAY ARE:

17) Prove that: \(G=\dfrac{3}{4}+\dfrac{5}{36}+\dfrac{7}{144}+...+\dfrac{2n+1}{n^2\left(n+1\right)^2}< 1\)

18) Prove that: \(L=\dfrac{1}{2!}+\dfrac{5}{3!}+\dfrac{11}{4!}+...+\dfrac{n^2+n-1}{\left(n+1\right)!}< 2\)



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    ¤« 24/03/2018 at 13:12

    17) G=34+536+7144+...+2n+1n2(n+1)2

    G=1−122+122−132+...+1n2−1(n+1)2

    G=1−1(n+1)2<1

     (proved)

  • ...
    Lê Quốc Trần Anh Coordinator 22/03/2018 at 11:10

    17) \(G=\dfrac{3}{4}+\dfrac{5}{36}+\dfrac{7}{144}+...+\dfrac{2n+1}{n^2\left(n+1\right)^2}\)

    \(G=1-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+...+\dfrac{1}{n^2}-\dfrac{1}{\left(n+1\right)^2}\)

    \(G=1-\dfrac{1}{\left(n+1\right)^2}< 1\) (proved)



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