Question

[hoang thi bich phuong]

Chứng tỏ:

A= 2 + 2^2 + 2^3 + ... + 2^50   3

B = 5 + 5^2 + 5^3 + ...+ 5^2016   31

C= 1 + 3 +3^2 + 3^5 +... + 3^2015  40

D = 7 + 7^2 + 7^3 + ... + 7^2016   57

Answer 1

[dhfdfeef]

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

A  =  2  (1+2)   +   2\(^2\)(1+2)   +   .....+   2\(^{49}\)(1+2)

A  =  ( 1+2  )(2+2\(^2\)+.....+2\(^{49}\))

A  =   3(2+2\(^2\)+.....+2\(^{49}\))  \(⋮\)3

Answer 2

[dhfdfeef]

B   =  (  5+  5\(^2\)+5\(^3\))  +  (5\(^4\)+  5\(^5\)+  5\(^6\))+....+(5\(^{2014}\)+  5\(^{2015}\)+  5\(^{2016}\))

B   =  5  (1+5+25)   +  5\(^4\)(1+5+25)  +....+5\(^{2014}\)(1+5+25)

B   =  (1+5+25)(5+5\(^4\)+....+5\(^{2014}\))

B   =   31(5+5\(^4\)+....+5\(^{2014}\))  \(⋮\)31