Question

Chứng tỏ:

A=1+3+3^{2 +}3³+...+3⁹⁹ chia hết cho 4

 

Answer 1

\(A=1+3+3^2+3^3+...+3^{99}\)

\(=\left(1+3\right)+\left(3^2+3^3\right)+...+\left(3^{98}+3^{99}\right)\)

\(=4+3^2.\left(1+3\right)+...+3^{98}.\left(1+3\right)\)

\(=4+3^2.4+...+3^{98}.4\)

\(=4.\left(1+3^2+...+3^{98}\right)\) chia hết cho 4

=> A chia hết cho 4 (đpcm).

Answer 2

= 1+3+3²+3³+..........+3⁹⁹+3¹⁰⁰

=(1+3)+(3²+3³+...........+3⁹⁹+3¹⁰⁰)

=3¹⁰⁰-4 chia het cho 4