Cho D=1/101+1/102+….+1/200 a,chứng minh D>7/12 b,chứng minh D>5/8 29/10/2021 Bởi aihong Cho D=1/101+1/102+….+1/200 a,chứng minh D>7/12 b,chứng minh D>5/8
Đáp án: Giải thích các bước giải: M=1/101+1/102+1/103+…+1/200 →M=(1/101+1/102+…+1/125)+(1/126+1/127+…+1/150)+(1/151+…+1/175)+(1/176+…+1/200) →M>(1 /125+1/125+…+1/125)+(1/150+1/150+..+1/150)+(1/200+..+1/200)+(1/200+..+1/200) →M>25/125+25/150+25/175+25/200 →M>1/5+1/6+1/7+1/8 →M>(1/5+1/6+1/7)+1/8 →M>107/210+1/8 →M>1/2+1/8=5/8 Vậy A=5/8 Bình luận
Đáp án:
Giải thích các bước giải:
M=1/101+1/102+1/103+…+1/200
→M=(1/101+1/102+…+1/125)+(1/126+1/127+…+1/150)+(1/151+…+1/175)+(1/176+…+1/200)
→M>(1 /125+1/125+…+1/125)+(1/150+1/150+..+1/150)+(1/200+..+1/200)+(1/200+..+1/200)
→M>25/125+25/150+25/175+25/200
→M>1/5+1/6+1/7+1/8
→M>(1/5+1/6+1/7)+1/8
→M>107/210+1/8
→M>1/2+1/8=5/8
Vậy A=5/8