Toán Lớp 6: cho S = 1/2 mũ 2 +1/3 mũ 2 +1/4 mũ 2 +…..+1/9 mũ 2. Chứng minh rằng 2/5
Toán Lớp 6: cho S = 1/2 mũ 2 +1/3 mũ 2 +1/4 mũ 2 +-.+1/9 mũ 2. Chứng minh rằng 2/5
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<1/2^2+1/2xx3+1/3xx4+….+1/8xx9
=1/2^2+1/2-1/3+1/3-1/4+….+1/8-1/9
=1/4+1/2-1/9=23/36<32/36=8/9 (a)
Ta lại có S=1/2^2+1/3^2+1/4^2+…+1/9^2
>1/2^2+1/3xx4+1/4xx5+….+1/9*10
=1/2^2+1/3-1/4+1/4-1/5+……..+1/9-1/10
=1/2^2+1/3-1/10
=19/20>8/20=2/5 ( a)