Question

Cho S= 1+3+3²+3³+3⁴+3⁵+3⁶+....+3²⁰¹⁵.

Chứng minh rằng: S chia hết cho 10.

Answer 1

\(S=\left(1+3+3^2+3^3\right)+\left(3^4+3^5+3^6+3^7\right)+...+\left(3^{2012}+3^{2013}+3^{2014}+3^{2015}\right)\)

\(=\left(1+3+9+27\right)+3^4.\left(1+3+3^2+3^3\right)+...+3^{2012}.\left(1+3+3^2+3^3\right)\)

\(=40+3^4.40+...+3^{2012}.40\)

\(=40.\left(1+3^4+...+3^{2012}\right)\)

\(=10.4.\left(1+3^4+...+3^{2012}\right)\text{ chia hết cho 10}\)

=> S chia hết cho 10 (đpcm).

Answer 2

chtt

Answer 3

S=(1+3+3^2)+(3^3+3^4+3^5)+...+(3^2013+3^2014+3^2015)

S=10+3^3(1+3+6)+...+3^2013(1+3+6)

S=10+3^3.10+...+3^2013.10

S=10(3^3+...+3^2013)

Vì tích trên có thừa số 10 mà 10 chia hết cho 10 nên S chia hết cho 10