Question

Tính \(A=1+5+5^2+...+5^{50}\)

Answer 1

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

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

\(\Rightarrow5A-A=\)\(\left(5+5^2+..+5^{51}\right)-\left(1+5+..+5^{50}\right)\)

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

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

Answer 2

Ta có : A = 1 + 5 + 5² + 5³ + ... + 5⁵⁰
=> 5A = 5 + 5² + 5³ + ... + 5⁵¹

=> 5A – A =( (5 + 5² + 5³ + ... + 5⁵¹ ) – (1 + 5 + 5² + 5³ + ... + 5⁵⁰) )

=> 4A = 5⁵¹ – 1

=> A = 5⁵¹ – 1 : 4

Answer 3

A = 1 + 5 + 5² + ... + 5⁵⁰

5A = 5 + 5² + 5³ + ... + 5⁵⁰ + 5⁵¹

5A – A = ( 5 + 5² + 5³ + 5⁴ + ... + 5⁵⁰ + 5⁵¹ ) – ( 1 + 5 + 5² + 5³ + 5⁴ + ... + 5⁵⁰ )

4A = 5⁵¹ –1

A =

Answer 4

A = 1 + 5 + 52 + ... + 550

\(\Rightarrow\) 5A = 5 + 52 + 53 + ... + 550 + 551

\(\Rightarrow\) 5A – A = ( 5 + 52 + 53 + 54 + ... + 550 + 551 ) – ( 1 + 5 + 52 + 53 + 54 + ... + 550 )

\(\Rightarrow\) 4A = 551 –1

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