Question

[Hoàng Phương Bích]

Cho A = 5 + 5^2 + 5^3 + 5^4.....+5^49 + 5^50

A,chứng minh răng 4.A = 5^51-5

B, Chứng A chia hết 6

Answer 1

[𝓗𝓾𝔂 ♪]

TL:

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

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

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

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

         \(4A=5^{51}-5\)

Vậy \(4A=5^{51}-5\left(đpcm\right)\)

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

          \(A=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{49}\left(1+5\right)\)

          \(A=5.6+5^3.6+...+5^{49}.6\)

           \(A=6.\left(5+5^3+...+5^{49}\right)⋮6\)

Vậy \(A\)chia hết cho 6 

HT!!~!