a,A=\(\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}\)

b,B=\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{998\times999\times100}\)

c,C=\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1\times98+2\times97+3\times96+...+98\times1}\)

Tính:

A = \(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+99\right)}{1\times99+2\times98+3\times97+...+99\times1}\)

 B = \(\frac{1\times2010+2\times2009+3\times2008+...+2010\times1}{\left(1+2+3+...+2010\right)+\left(1+2+3+...+2009\right)+...+\left(1+2\right)+1}\)

\(\frac{1+< 1+2>+< 1+2+3>+..............+< 1+2+3+4+...........+98>}{1\times98+2\times97+3\times96+..............................+98\times1}\)

Giúp mình nhé ai nhanh nhất mình tíck

Cho B=\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1\cdot98+2\cdot97+3\cdot96+...+98\cdot1}\)

Rút gọn B ta được B=

rút gọn \(B=\frac{1+\left(1+2\right)+\left(1+2+3\right)+.........+\left(1+2+3+.......+98\right)}{1\cdot98+2\cdot97+3\cdot96+........+98\cdot1}\)

Cho B=\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1.98+2.97+3.96+...+98.1}\). Rút gọn B ta được B=..........

Cho B=\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1.98+2.97+3.96+...+98.1}\)  Rút gọn B ta được B=

Tính

\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+99+100\right)}{\left(1\times100+2\times99+3\times98+...+99\times2+100\times1\right)\times2013}\)

Cho \(B=\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1.98+2.97+3.96+...+98.1}\)

Rút gọn B.