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A=2^2/1.3+3^2/2.4+4^2/3.5+....+99^2/98.100
A=2^2/(2-1)(2+1)+3^2/(3-1)(3+1)+4^2/(4-1)(4+1)+...+99^2/(99-1)(99+1)
A=2^2/2^2-1+3^2/3^2-1+...+99^2/99^2-1
A=2^2-1+1/2^2-1+3^2-1+1/3^2-1+...+99^2-1+1/99^2-1
A=1+1/1.3+1+1/2.4+1+1/3.5+...+1+1/98.100
A=(1+1+1+....+1)+(1/1.3+1/2.4+...+1/98.100) (1)
Ta có:
Đặt B=(1+1+1+...+1)=98[vì (99-2):1+1=98 số] (2)
Đặt C=1/1.3+1/2.4+1/3.5+...+1/98.100
=>C=1/2.(1-1/3)+1/2.(1/2-1/4)+1/2.(1/3-1/5)+...+1/2.(1/98-1/100)
=>C=1/2.(1-1/3+1/2-1/4+1/3-1/5+...+1/97-1/99+1/98-1/100)
=>C=1/2.(1+1/2-1/99-1/100)
=>C=1/2.(3/2-1/99.100) (3)
Thay (2),(3) vào(1), được:
A=98+1/2.(3/2-1/99.100)
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\(2^3+3.\left(\frac{1}{9}\right)^0-2.4+\left[\left(-2\right)^2:\frac{1}{2}\right].8\)
\(=8+3.1-8+\left(4:\frac{1}{2}\right).8\)
\(=\left(8-8\right)+3+8.8\)
\(=3+64=67\)
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