Question

1+5+5^2+5^3+5^4+.....+5^49+5^50

Answer 1

#)Giải :

Đặt \(A=1+5+5^2+5^3+5^4+...+5^{49}+5^{50}\)

\(\Rightarrow5A=5+5^2+5^3+5^4+...+5^{50}+5^{51}\)

\(\Rightarrow5A-A=4A=\left(5+5^2+5^3+...+5^{50}+5^{51}\right)-\left(1+5+5^2+5^3+...+5^{49}+5^{50}\right)\)

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

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

Answer 2

Đặt S = 1 + 5 + 5² + 5³ + 5⁴ + ........ + 5⁴⁹ + 5⁵⁰
     5S = 5 + 5² +5³⁺ 5⁴ + 5⁵ + ........ + 5⁵⁰ +5⁵¹
5S - S = (5 + 5² +5³⁺ 5⁴ + 5⁵ + ........ + 5⁵⁰ +5⁵¹) - (1 + 5 + 5² + 5³ + 5⁴ + ........ + 5⁴⁹ + 5⁵⁰)
     4S =5⁵¹ - 1 
       S =(5⁵¹- 1) : 4
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Answer 3

Gọi \(A=1+5+5^2+5^3+5^4+...+5^{49}+5^{50}\)

\(A=1+5+5^2+5^3+5^4+...+5^{49}+5^{50}\)

\(5A=5+5^2+5^3+5^4+...+5^{49}+5^{50}+5^{51}\)

\(5A-A=\left(5+5^2+5^3+5^4+...+5^{49}+5^{50}+5^{51}\right)-\left(1+5+5^2+5^3+5^4+...+5^{49}+5^{50}\right)\)

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

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

Answer 4

A = 1 + 5 + 5² + 53 + 5⁴ + ...+ 5⁴⁹ + 5⁵⁰ (1)

Nhân 2 vế với 5 ta có :

5A=5(1+5+5²+5³+...+5⁵⁰)

5A=5+5²+5³+.....+5⁵⁰+5⁵¹ (2)

LẤY  (2)-(1) TA CÓ :

5A=5+5²+5³+....+5⁵¹

-A=1+5+5²+....+5⁵⁰

4A=5⁵¹-1

A=\(\frac{5^{51}-1}{4}\)
 

Answer 5

Có A = 1 + 5 + 5² + 5³ + ... + 5⁴⁹ + 5⁵⁰

=> 5A = 5.(1 + 5 + 5² + 5³ + ... + 5⁴⁹ + 5⁵⁰)

          = 5 + 5² + 5³ + 5⁴ + ..... + 5⁵⁰ + 5⁵¹

=> 5A - A = (5 + 5² +5³ + 5⁴ +... + 5⁵⁰ + 5⁵¹) - (1 + 5 + 5² + 5³ + .... + 5⁴⁹ + 5⁵⁰)

=> 4A = 5⁵¹ - 1

=> A = \(\frac{5^{51}-1}{4}\)