Question

Tính A= 1+5+5^2+....+5^49+5^50

Answer 1

\(A=1+5+5^2+5^3+.....+5^{49}+5^{50}\)

\(\Rightarrow5A=5+5^2+5^3+5^4+...+5^{50}+5^{51}\)

\(5A-A=\left(5+5^2+5^3+5^4+...+5^{50}+5^{51}\right)-\left(1+5+5^2+5^3+....+5^{49}+5^{50}\right)\)

\(\Rightarrow4A=5^{51}-1\)

\(A=\frac{5^{51}-1}{4}\)

Answer 2

A = 1 + 5 + 5² + .... + 5⁴⁹ + 5⁵⁰

5A = 5 + 5² + 5³ + ... + 5⁵⁰ + 5⁵¹

5A - A = (5 + 5² + 5³ + ... + 5⁵⁰ + 5⁵¹)  - (1 + 5 + 5² + .... + 5⁴⁹ + 5⁵⁰)

4A = 5⁵¹ - 1

\(A=\frac{5^{51}-1}{4}\)