Question

Rút Gọn A = 5 + 5^2 + 5^3 + .......... 5^50


Rút Gọn Giúp Mình Với Gấp Gấp

Answer 1

A = 5 + 5 ^ 2 + 5 ^ 3 + ... + 5 ^ 50

5 A = 5 ^ 2 + 5 ^ 3 + 5 ^ 4 + ... + 5 ^ 51

5 A - A = ( 5 ^ 2 + 5 ^ 3 + 5 ^ 4 + ... + 5 ^ 51 )

            -  ( 5 + 5 ^ 2 + 5 ^ 3 + ... + 5 ^ 50 )

4 A      = 5 ^ 51 - 5

A         = \(\frac{5^{51}-5}{4}\)

Answer 2

A=5^1+5^21+5^3+...+5^50

5^1A=5(5^1+5^2+5^3+..+5^50)

5A=5^2+5^3+..+5^50+5^51

5A-A=(5^2+5^3+..+5^50+5^51)-(5^1+5^2+5^3+..+5^50)

4A=5^51-5^1

A=(5^51-5^1):4