Question

Cho P= 5¹+5²+5³+..........+5⁹⁸+5⁹⁹+5¹⁰⁰

a) CM: Pchia hết cho 30

Answer 1

\(P=\left(5+5^2\right)+5^2\left(5+5^2\right)+....+5^{98}\left(5+5^2\right)=30\left(1+5^2+....+5^{98}\right)\) chia hết cho 30

=>P chia hết cho 30

=>đpcm

Answer 2

P= 5¹+5²+5³+..........+5⁹⁸+5⁹⁹+5¹⁰⁰

P= (5¹+5²)+(5³+5⁴)+..........+(5⁹⁹+5¹⁰⁰)

P= (5¹+5²)(1+5²+..........+5⁹⁷+5⁹⁸+5⁹⁹)

P=30.(1+5²+..........+5⁹⁷+5⁹⁸+5⁹⁹)chia hết cho 30