Question

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

Answer 1

Ta có : A = 1 + 5 + 5² + ...... + 5⁴⁹ + 5⁵⁰

=> 5A = 5 + 5² + 5³+..... + 5⁵⁰ + 5⁵¹

=> 5A - A = 5⁵¹ - 1

=> 4A = 5⁵¹ - 1

=> \(A=\frac{5^{51}-1}{4}\)

Answer 2

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

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

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

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

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