Câu hỏi của Trinh Van Nguyen

Question

Tính S=(-1/7)^0+(-1/7)^1+(-1/7)^2+....+(-1/7)^2016

Nguyễn Xuân Tiến 24 · Accepted Answer

S=($\dfrac{-1}{7}$)0+($\dfrac{-1}{7}$)1+...+($\dfrac{-1}{7}$)2016

$\Rightarrow$$\dfrac{-1}{7}S$=($\dfrac{-1}{7}$)1+($\dfrac{-1}{7}$)2+...+($\dfrac{-1}{7}$)2017

$\Rightarrow$$\dfrac{-1}{7}S$-$S$=$[$ ($\dfrac{-1}{7}$)1+($\dfrac{-1}{7}$)2+...+

($\dfrac{-1}{7}$)2017 $]$-$[$($\dfrac{-1}{7}$)0+($\dfrac{-1}{7}$)1+...+

($\dfrac{-1}{7}$)2016$]$

=($\dfrac{-1}{7}$)1+($\dfrac{-1}{7}$)2+...+($\dfrac{-1}{7}$)2017-

($\dfrac{-1}{7}$)0-($\dfrac{-1}{7}$)1-...-($\dfrac{-1}{7}$)2016

$\dfrac{-8}{7}S$=($\dfrac{-1}{7}$)2017-1

S=$\dfrac{(\dfrac{-1}{7})^{2017}-1}{\dfrac{-8}{7}}$Câu trả lời: S=($\dfrac{-1}{7}$)0+($\dfrac{-1}{7}$)1+...+($\dfrac{-1}{7}$)2016