Question

giải cho S= 1-5+5mũ2 - 5mũ3 +...... + 5 mũ 58 -5 mũ 59

Answer 1

\(S=1-5+5^2-5^3+...+5^{58}-5^{59}\)

\(5.S=5-5^2+5^3-5^4+...+5^{59}-5^{60}\)

\(5.S-S=1-5^{60}\)

\(4.S=1-5^{60}\)

\(S=\frac{1-5^{60}}{4}\)

Vậy\(S=\frac{1-5^{60}}{4}\)​​

Answer 2

S = 1 - 5 + 5² - 5³ + ... + 5⁵⁸ - 5⁵⁹

5S = 5 - 5² + 5³ - 5⁴ + ... + 5⁵⁹ - 5⁶⁰

5S - S = (5 - 5² + 5³ - 5⁴ + ... + 5⁵⁹ - 5⁶⁰) - 1 - 5 + 5² - 5³ + ... + 5⁵⁸ - 5⁵⁹

4S = 5⁶⁰ - 1

=> S = \(\frac{5^{60}-1}{4}\)