Question

Cho S= 5/2²+5/3²+5/4²+...+5/100². Chứng minh 2<S<5

Answer 1

5/2² + 5/3² + 5/4² +...+ 5/100² < 5/1.2 + 5/2.3 +5/3.4 +...+ 5/99.100

5/2.2 +5/3.3 + 5/4.4 +...+ 5/100.100 < 5. ( 1/1.2 + 1/2.3 +1/3.4 +..+ 1/99.100)

5/2.2 +5/3.3 + 5/4.4 +...+ 5/100.100 < 5. (1/1 -1/2 +1/2 -1/3 +1/3-1/4 +...+ 1/99-1/100)

5/2.2 +5/3.3 + 5/4.4 +...+ 5/100.100 < 5. (1/1-1/100)

5/2.2 +5/3.3 + 5/4.4 +...+ 5/100.100 < 5. ( 100/100 -1/100)

5/2.2 +5/3.3 + 5/4.4 +...+ 5/100.100 < 5. 99/100

5/2.2 +5/3.3 + 5/4.4 +...+ 5/100.100 < 99/20

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