2^50.(1/2-1/3).(1/2-1/5).(1/2-1/7). ... .(1/2-1/101)
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\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}=1-\dfrac{1}{101}=\dfrac{100}{101}\)
\(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{99\cdot101}\\ =1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\\ =1-\dfrac{1}{101}=\dfrac{100}{101}\)
a: x/3-1/6=1/5
=>x/3=11/30
hay x=11/90
b: =>1/2x=2
hay x=4
c: =>2/3:x=-7-1/3=-22/3
=>x=-1/11
a, -1+3 - 5 + 7 - ...... +97 - 99
[ - 1+ 3] - [ 5 + 7] - .... - [ 95 + 97] - 99
[2 - 12] - ..... - [184 - 192] - 99
còn lại tự giải
a)
(1/3-1/5)x1/4 = 1/3x1/4-1/5x1/4=1/12-1/20=1/30
(1/3-1/5)x1/4 = 2/15x1/4=1/30
b)
2/5 x 3/7 + 2/5 x 4/7= 6/35 + 8/35 = 14/35 = 2/5
2/5 x 3/7 + 2/5 x 4/7= (3/7+4/7) x 2/5 = 1 x 2/5 = 2/5
a: C1: (1/3-1/5)*1/4
=2/15*1/4=2/60=1/30
C2: (1/3-1/5)*1/4
=1/3*1/4-1/5*1/4
=1/12-1/20=1/30
b: C1: 2/5*3/7+2/5*4/7
=6/35+8/35=14/35=2/5
C2: 2/5*3/7+2/5*4/7
=2/5(3/7+4/7)
=2/5*1=2/5
\(A=\frac{\left[\left(25-1\right):1+1\right]\left(25+1\right)}{2}=325.\)
\(B=\frac{\left[\left(51-3\right):2+1\right]\left(51+3\right)}{2}=675\)
\(C=\frac{\left[\left(81-1\right):4+1\right]\left(81+1\right)}{2}=861\)
S = 1/5^2 - 1/5^3 +1/5^4 -1/5^5 +... - 1/5^101
5^2.S = 5^2. ( 1/5^2 - 1/5^3 +1/5^4 -1/5^5 +... - 1/5^101)
25 .S =1-1/5^2+1/5^3-1/5^4+..-1/5^100
25S+S = (1-1/5^2+1/5^3-1/5^4+..-1/5^100)+( 1/5^2 - 1/5^3 +1/5^4 -1/5^5 +... - 1/5^101)
26S=1-1/5^101
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