Btinh gia tri bieu thuc B=(1/2^2 -1) . ( 1/3^2-1) .(1/4^2 -1) . ... .(1/98 ^2 -1) . (1/99^2 -1)
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tinh tong gia tri bieu thuc :
a)A=1+1/3+1/5+...+1/97+1/99/1/1*99+1/3*97+1/5*95+...+1/97*3+1/99*1
b)B=1/2+1/3+1/4+...+1/100/99/1+98/2+97/3+...+1/99
tinh gia tri bieu thuc : a ) : (1+2+3+4+ .............+97+98+99+100) : 5
Tổng các số trong trong ngoặc là:(100+1).[(100-1):1+1]:2=5050
a=5050:5=1010
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TINH GIA TRI CUA BIEU THUC
a: A=100-99+98-97....+4 -3 +2=.......
b:B =1+1+1+.......+1 -999(CO 1000 SO 1)=.......
Tinh gia tri bieu thuc
D = -1/3 +1/32-1/33+..........+1/398-1/399
\(D=\left(-\dfrac{1}{3}\right)^1+\left(-\dfrac{1}{3}\right)^2+...+\left(-\dfrac{1}{3}\right)^{98}+\left(\dfrac{-1}{3}\right)^{99}\)
\(\Leftrightarrow\left(-\dfrac{1}{3}D\right)=\left(-\dfrac{1}{3}\right)^2+...+\left(-\dfrac{1}{3}\right)^{99}+\left(-\dfrac{1}{3}\right)^{100}\)
\(\Leftrightarrow D\cdot\dfrac{-4}{3}=\dfrac{1^{100}}{3^{100}}-\left(-\dfrac{1}{3}\right)=\dfrac{1}{3^{100}}+\dfrac{1}{3}=\dfrac{1+3^{99}}{3^{100}}\)
\(\Leftrightarrow D=\dfrac{3^{99}+1}{3^{100}}:\dfrac{-4}{3}=\dfrac{3^{99}+1}{-4\cdot3^{99}}\)
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tinh gia tri bieu thuc [1+1/100] * [1+1/99]*.....* [1+1/3] * [1+1/2]
Ta có : \(\left(1+\frac{1}{100}\right).\left(1+\frac{1}{99}\right).......\left(1+\frac{1}{3}\right)\left(1+\frac{1}{2}\right)\)
\(=\frac{101}{100}.\frac{100}{99}.\frac{99}{98}......\frac{4}{3}.\frac{3}{2}=\frac{101}{2}\)
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\(\left(1+\frac{1}{100}\right).\left(1+\frac{1}{99}\right).....\left(1+\frac{1}{3}\right).\left(1+\frac{1}{2}\right)\)
\(=\frac{101}{100}.\frac{100}{99}.....\frac{4}{3}.\frac{3}{2}=\frac{101}{2}\)
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Đặt \(A=\left[1+\frac{1}{100}\right]\cdot\left[1+\frac{1}{99}\right]\cdot....\cdot\left[1+\frac{1}{3}\right]\cdot\left[1+\frac{1}{2}\right]\)
\(A=\frac{101}{100}\cdot\frac{100}{99}\cdot....\cdot\frac{4}{3}\cdot\frac{3}{2}\)
\(A=\frac{101}{\frac{4}{2}}=\frac{101}{2}\)
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Tinh gia tri bieu thuc
1+ 1+ 1+.................................... +1
(1*2)+(2*3)+(3*4).................................+(99*100)
cho bieu thuc a=-1/3+1/3^2-1/3^3+1/3^4-1/3^5+...+1/3^100 tinh gia tri cua bieu thuc b=4/a/+1/3^100
cho x+y =1 . tinh gia tri cua bieu thuc A=x^3+y^3+3xy
chox-y=1. tinh gia tri cua bieu thuc B=x^3-y^3-3xy
cho x+y=1 . tinh gia tri cua bieu thuc C=x^3+y^3+3xy(x^2+y^2)+6x^2*y^2(x+y)
Câu 1: Ta có: A = \(x^3+y^3+3xy=x^3+y^3+3xy\times1=x^3+y^3+3xy\left(x+y\right)\)
\(=\left(x+y\right)^3=1^3=1\)
Câu 2: Ta có: \(B=x^3-y^3-3xy=\left(x-y\right)\left(x^2+xy+y^2\right)-3xy\)
\(=x^2+xy+y^2-3xy=x^2-2xy+y^2=\left(x-y\right)^2=1^2=1\)
Câu 3: Ta có: \(C=x^3+y^3+3xy\left(x^2+y^2\right)-6x^2.y^2\left(x+y\right)\)
\(=x^3+y^3+3xy\left(x^2+2xy+y^2-2xy\right)+6x^2y^2\)
\(=x^3+y^3+3xy\left(x+y\right)^2-3xy.2xy+6x^2y^2\)
\(=x^3+y^3+3xy.1-6x^2y^2+6x^2y^3\)
\(=x^3+y^3+3xy\left(x+y\right)=\left(x+y\right)^3=1^3=1\)
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tim gia tri cua bieu thuc
A=1-2-3-4+5-6-7-8+9-10-11-12+...........+97+98-99-100