Question

Rút gọn

A = 1 + + 5 + 5² + 5³ + ... + 5⁴⁹ + 5⁵⁰

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

GIÚP TÔI NHA!

CÁC BẠN CÓ THỂ LÀM 1 TRONG 2 BÀI CŨNG ĐƯỢC

Answer 1

\(A=1+5+5^2+5^3+...+5^{49}+5^{50}\)
\(5A=5^1+5^2+5^3+5^4+...+5^{51}\)
\(4A=5A-A=5^{51}-1\)
\(\Rightarrow A=\frac{5^{51}-1}{4}\)
b/
\(B=\frac{1}{2}+\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+...+\left(\frac{1}{2}\right)^{98}+\left(\frac{1}{2}\right)^{99}\)
\(\frac{1}{2}B=\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+\left(\frac{1}{2}\right)^4+...+\left(\frac{1}{2}\right)^{100}\)
\(\frac{1}{2}B=B-\frac{1}{2}B=\frac{1}{2}-\left(\frac{1}{2}\right)^{100}\)
\(B=\frac{1}{2}B\cdot2=\left[\frac{1}{2}-\left(\frac{1}{2}\right)^{100}\right].2\)
\(B=1-\frac{1}{2^{99}}\)