Toán Lớp 6: Chứng minh rằng: 1/1^2+1/2^2+1/3^2+…+1/100^2 >100/101
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Toán Lớp 6: Chứng minh rằng: 1/1^2+1/2^2+1/3^2+…+1/100^2 >100/101
Comments ( 2 )
Đặt:
S= 1/1^2+1/2^2+1/3^2+…+1/100^2
Theo bài ra ta có:
1/1^2=1/1.1>1/1.2=1-1/2
1/2^2=1/2.2>1/2.3=1/2-1/3
……………………
1/100^2=1/100.100>1/100.101=1/100-1/101
=>A>1-1/2+1/2-1/3+…+1/100-1/101
=>A>1-1/101
=>A>101/101-1/101
=>A>100/101
Vậy A>100/101