ta có: 2B=\(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+..+\frac{1}{2^{97}}+\frac{1}{2^{98}}\)

B=\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+..+\frac{1}{2^{98}}+\frac{1}{2^{99}}\)

=>2B-B=\(1-\frac{1}{2^{99}}\)

mà 1/2^99>0 nên B<1 (đpcm)

C = 1/3 + 1/3^2 + 1/3^3 + ... =1/3^99

=> C = 1/3^99 = 1/(3^99) 

=> C < 1/2 (đpcm) 

2A=2^101-2^100+2^98+...+2^3-2^2

3A = 2A + A

3A = 2^101 - 2 ( Cứ tính là ra , âm vs dương triệt tiêu )

A = (2^101-2) :3

B tăng tự 

A=2^100-2^99+2^98-2^97+...+2^2-2

=>2A=2¹⁰¹-2¹⁰⁰+2⁹⁹-2⁹⁸+...+2³-2²

=>A+2A=2¹⁰⁰-2⁹⁹+2⁹⁸-2⁹⁷+...+2²-2+2¹⁰¹-2¹⁰⁰+2⁹⁹-2⁹⁸+...+2³-2²

=>3A=2¹⁰¹-2

=>A=\(\frac{2^{101}-2}{3}\)

Bạn tham khảo nhé:

\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)

\(\Rightarrow2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)

\(\Rightarrow2A+A=2^{101}-2^{100}+...+2^3-2^2+2^{100}-2^{99}+...+2^2-2\)

\(\Rightarrow3A=2^{101}-2\)

\(\Rightarrow A=\frac{2^{101}-2}{3}\)

 Chúc bạn học tốt!