giúp em với mọi người ơi,có mỗi một câu thôi trả lời xong cho hay nhất

2A=1+$\frac{2}{2}$+ $\frac{3}{2^{2}}$+...+ $\frac{30}{2^{29}}$ 

2A-A=(1+$\frac{2}{2}$+ $\frac{3}{2^{2}}$+...+ $\frac{30}{2^{29}}$)-($\frac{1}{2}$+ $\frac{2}{2^{2}}$+ $\frac{3}{2^{3}}$+...+ $\frac{30}{2^{30}}$ )

A=1+$\frac{1}{2}$+ $\frac{1}{2^{2}}$+...+ $\frac{1}{2^{29}}$- $\frac{30}{2^{30}}$ 

 Đặt B=1+$\frac{1}{2}$+ $\frac{1}{2^{2}}$+...+ $\frac{1}{2^{29}}$

2B=2+1+$\frac{1}{2}$+ $\frac{1}{2^{2}}$+...+ $\frac{1}{2^{28}}$

2B-B=(2+1+$\frac{1}{2}$+ $\frac{1}{2^{2}}$+...+ $\frac{1}{2^{28}}$)-(1+$\frac{1}{2}$+ $\frac{1}{2^{2}}$+...+ $\frac{1}{2^{29}}$)

B=2-$\frac{1}{2^{29}}$=$\frac{2^{30}-1}{2^{29}}$ 

⇒A=$\frac{2^{30}-1}{2^{29}}$- $\frac{30}{2^{30}}$= $\frac{2^{31}-2-30}{2^{30}}$= $\frac{2^{31}-32}{2^{30}}$ =$\frac{2^{31}-2^{5}}{2^{30}}$= $\frac{2^{26}-1}{2^{25}}$