Question

Tính: B=1+5+5^2++5^3+...+5^19+5^20

Answer 1

\(B=1+5+5^2+5^3+...+5^{19}+5^{20}\)

\(\Rightarrow5B=5+5^2+5^3+5^4+...+5^{20}+5^{21}\)

\(\Rightarrow5B-B=\left(5+5^2+5^3+...+5^{20}+5^{21}\right)-\left(1+5+5^2+...+5^{19}+5^{20}\right)\)

\(\Rightarrow4B=5^{21}-1\Rightarrow B=\frac{5^{21}-1}{4}\)

Answer 2

B = 1 + 5 + 5² + 5³ + ... + 5¹⁹ + 5²⁰

5B = 5 + 5² + 5³ + 5⁴ + ... + 5²⁰ + 5²¹

5B - B = (5 + 5² + 5³ + 5⁴ + ... + 5²⁰ + 5²¹) - (1 + 5 + 5² + 5³ + ... + 5¹⁹ + 5²⁰)

4B = 5²¹ - 1

B = \(\frac{5^{21}-1}{4}\)