Toán Lớp 6: CHỨNG TỎ: 1/3 mũ 2+ 1/4 mũ 2+ 1/5 mũ 2+… +1/100 <1/2
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Toán Lớp 6: CHỨNG TỎ: 1/3 mũ 2+ 1/4 mũ 2+ 1/5 mũ 2+… +1/100 <1/2
Comments ( 2 )
1/3^2<1/2.3
1/4^2<1/3.4
1/5^2<1/4.5
…
1/100^2<1/99.100
=>1/3^2+1/4^2+1/5^2+…+1/100^2<1/2.3+1/3.4+1/4.5+…+1/99.100
=>1/3^2+1/4^2+1/5^2+…+1/100^2<1/2-1/3+1/3-1/4+1/4-1/5+…+1/99-1/100
=>1/3^2+1/4^2+1/5^2+…+1/100^2<1/2-1/100<1/2(ĐPCM)
Vậy 1/3^2+1/4^2+1/5^2+…+1/100^2<1/2