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\(B=\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2012}\)
\(B=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1006}\right)\)
\(B=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2012}\right)\)
\(B=1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2011}-\frac{1}{2}-\frac{1}{4}-...-\frac{1}{2012}\)
\(B=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2011}-\frac{1}{2012}\)
a ) 13/20
B)
C..........................................................
minh dang tính
Các cậu ơi giúp tớ với nka:
Cho A=1-1/2+1/3-1/4+...-1/2012;B=1/1007+1/1008+...+1/2012. Tính (A/B)2013
A=1-(1-1/2)+1/3-(1/2-1/4)+..-(1/1006-1/2012)
A=1-1+1/2+1/3-1/2+1/4+...-1/1006+1/2012
A=(1-1)+(1/2-1/2)+...+(1/1006-1/1006)+1/1007+1/1008+..+1/2012
A=B => (A/B)^2013=1
Học tốt
\(Xét:1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...-\frac{1}{2012}\)
\(=\left(1+\frac{1}{3}+...+\frac{1}{2011}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)
\(=\left(1+\frac{1}{3}+...+\frac{1}{2011}\right)\)\(+\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)\(-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)\(+\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)\)\(-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)\)\(-\left(1+\frac{1}{2}+...+\frac{1}{1006}\right)\)
\(=\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2012}\)
\(\RightarrowĐPCM\)
7 . (-2)^3 - 60:15
= 7 . (-8) - 4
= (-56)- 4
= - 60
125 - (-75) + 32 - (48 + 32)
= 125-75 + 32 - 48 -32
= 50 + (-48)
=2
A = 47 x 36 + 64 x 47 + 15
A= 47 x ( 64 + 36 ) + 15 = 47 x 100 + 15 = 4700 + 15 = 4715
vậy A= 4715
B= 27+35 + 65 + 73+ 75
B= (27+ 73) + ( 35 + 65) +75
B= 100 +100 +75 = 275
vậy B= 275
C= 37 +37 x 15 +37 x 84
C= 37 x ( 1+15 +84 )= 37 x 100 = 3700
vậy C= 3700
D = 1/20x21 + 1/21x22 + 1/22x23 + 1/23x24
D= 1/20 - 1/21 + 1/21 - 1/22 + 1/22 - 1/23 + 1/23 - 1/24
D= 1/20 -1/24 = 1/120 vậy D= 1/120
E= 1/1x2 + 1/2x3 + ...... + 1/49x50
E= 1/1 - 1/2 + 1/2 - 1/3 +...... + 1/49 - 1/50
E = 1 - 1/50 = 49/50
vậy E= 49/50
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