cmr
100-(1+1/2+1/3+...+1/100)=1/2+2/3+3/4+....+99/100
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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+1/2+1/3+1/4+...+1/100)=1/2=2/3+3/4+...+99/100
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) 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16
CMR(1/1*2+1/2*3+1/3*4+1/4*5+...+1/99*100):(1/51+1/52+1/53+...+1/100) = 1
Sửa đề: \(\dfrac{\dfrac{1}{1\cdot2}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}}{\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{100}}\)
\(=\dfrac{1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}}{\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{100}}\)
\(=\dfrac{\left(1+\dfrac{1}{3}+...+\dfrac{1}{99}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)}{\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{100}}\)
\(=\dfrac{\left(1+\dfrac{1}{3}+...+\dfrac{1}{99}\right)+\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)-2\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)}{\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{100}}\)
=1
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CMR:
a)1/2-1/4+1/8-1/16+1/32-1/64<1/3
b)1/3 - 2/3^2 + 3/3^3 - 4/3^4 +...+ 99/3^99 -100/3^100 < 3/16
cmr
a) 1/2 -1/4+1/8-1/16+1/32-1/64 <1/3
b) 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16
CMR 100 - ( 1 + 1/2 + 1/3 + ... + 1/100 ) = 1/2 + 2/3 + ... + 99/100.
CMR : 1/3 - 2/3^2 + 3^3 - 4/3^4 + .... + 99/3^99 - 100/3^100 < 3/16