Question

Tính C=5+5 mũ 2+5 mũ3+5 mũ 4+...+5 mũ 99+5 mũ 100

Answer 1

Ta có : C = 5 + 5² + 5³ + 5⁴ + ....... + 5¹⁰⁰

=> 5C = 5. (5 + 5² + 5³ + 5⁴ + ....... + 5¹⁰⁰)

=> 5C = 5² + 5³ + 5⁴ + ....... + 5¹⁰¹

=> 5C - C = 5¹⁰¹ - 5

=> 4C = 5¹⁰¹ - 5

=> C = \(\frac{5^{101}-5}{4}\)

Answer 2

\(C=5+5^2+5^3+5^4+...+5^{100}\)

\(5C=5^2+5^3+5^4+5^5+...+5^{101}\)

\(5C-C=\left(5^2+5^3+5^4+5^5+...+5^{101}\right)-\left(5+5^2+5^3+5^4+...+5^{100}\right)\)

\(4C=5^{101}-5\)

\(C\left(5^{101}-5\right):4\)