Question

Rút gọn  

A = 1+2^2+.............2^100

B=5^1+5^2+.....................5^199

Answer 1

A=1+2^2+...+2^100

2A=2+2^2+2^3+...+2^101

2A=2^101-1

A=(2^101-1):2

Answer 2

\(B=5^1+5^2+...+5^{199}\)

\(\Rightarrow5B=5^2+5^3+...+5^{200}\)

\(\Rightarrow5B-B=\left(5^2+5^3+...+5^{200}\right)-\left(5^1+5^2+...+5^{199}\right)\)

\(\Rightarrow4B=5^{200}-5\)

\(\Rightarrow B=\frac{5^{200}-5}{4}\)