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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 7: Cho S = 1/2^2+1/3^2+1/4^2+..+1/2020^2 chứng tỏ s<1 mik cần gấp ạ

Toán Lớp 7: Cho S = 1/2^2+1/3^2+1/4^2+..+1/2020^2
chứng tỏ s<1 mik cần gấp ạ

Comments ( 1 )

  1. Ta có : S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+…+\frac{1}{2020^2} < \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..+\frac{1}{2019.2020}
    =>S<1-1/2+1/2-1/3+1/3-1/4+…+1/2019-1/2020
    =>S<1-1/2020<1
    =>\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+…+\frac{1}{2020^2}<1

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222-9+11+12:2*14+14 = ? ( )