Question

 S=7^1+7^2+7^3+.............+7^2016

a,Thu gọn S

b,Chứng minh S chia hết cho 35

Answer 1

S = \(7+7^2+.............+7^{2016}\)

\(7S=7^2+7^3+...........+7^{2017}\)

\(7S-S=\left(7^2-7^2\right)+\left(7^3-7^3\right)+...........+7^{2017}-7\)

\(S=\frac{7^{2017}-7}{6}\)

b) \(S=\left(7+7^2+7^3+7^4\right)+.............+\left(7^{2013}+7^{2014}+7^{2015}+7^{2016}\right)\)

\(S=35.2^4.5+35.2^4.5.7^4+.........+35.2^4.5.7^{2012}\)

\(S=35.2^4.5.\left(1+7^4+7^8+............+7^{2012}\right)\)

Vậy chia hết cho 35          

Answer 2

đề đúng không vậy Nguyễn Tuấn Tài