cmr 1/2+2/2^2+3/2^3+...+100/2^100<2
Những câu hỏi liên quan
CMR 100 - ( 1 + 1/2 + 1/3 + ... + 1/100 ) = 1/2 + 2/3 + ... + 99/100.
cmr
100-(1+1/2+1/3+...+1/100)=1/2+2/3+3/4+....+99/100
\(=\left(1-1\right)+\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{3}\right)+...+\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{99}{100}\)
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cmr 100-(1+1/2+1/3+...+1/100)=1/2+2/3+...+99/100
Ta có :
\(100-\left(1+\frac{1}{2}+\frac{1}{3}+.....+\frac{1}{100}\right)=1.100-\left(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{100}\right)\)
\(=\left(1-1\right)+\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{3}\right)+.......+\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}+\frac{2}{3}+.........+\frac{99}{100}\)
Vậy \(100-\left(1+\frac{1}{2}+\frac{1}{3}+......+\frac{1}{100}\right)=\frac{1}{2}+\frac{2}{3}+.....+\frac{99}{100}\left(ĐPCM\right)\)
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CMR 1/3-2/3^2+3/2^3-....+100/2^100<3/16
CMR:
a)1/10^2 +1/11^2+1/12^2+...+1/100^2 >3/4
b)1/2^2+1/3^2+1/4^2+...+1/100^2<99/100
c)1/2^2+1/3^2+1/4^2+...+1/100^2<3/4
CMR:(1+1/2+1/3+1/4+...+1/100)=1/2=2/3+3/4+...+99/100
CMR
100-(1/2+1/3+1/4+...+1/100)=2/3+3/4+...+99/100
100=10*10
100=1000:10
100 câu nói hay về cuộc sống
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CMR 1/3-2/3^2+3/3^3-.....+100/3^100
CMR
1/2-2/2^2+3/2^3-4/2^4+.....+99/2^99-100/2^100<2/9