Question

Tìm x, biết:

a, | |x+5| - 4 | = 3

b, | x - 1 | = 2x - 5

c, | 3 - 8x | \(\ge\) 19

Tính

\(\dfrac{1}{3}\) - \(\dfrac{1}{3^2}\)+ \(\dfrac{1}{3^3}\)- \(\dfrac{1}{3^4}\)+ ... + \(\dfrac{1}{3^{2015}}\)- \(\dfrac{1}{3^{2016}}\)

Ai hok giỏi toán giúp mình bài nè vơi nha minh cần gấp

Answer 1

Đặt \(A=\dfrac{1}{3}-\dfrac{1}{3^2}+\dfrac{1}{3^3}-\dfrac{1}{3^4}+......+\dfrac{1}{3^{2015}}-\dfrac{1}{3^{2016}}\)

\(3A=1-\dfrac{1}{3}+\dfrac{1}{3^2}-\dfrac{1}{3^3}+\dfrac{1}{3^4}-......+\dfrac{1}{3^{2014}}-\dfrac{1}{3^{2015}}\)

\(3A+A=4A=1-\dfrac{1}{3^{2016}}\)

\(A=\dfrac{1-\dfrac{1}{3^{2016}}}{4}=\dfrac{\dfrac{3^{2016}-1}{3^{2016}}}{4}=\dfrac{3^{2016}-1}{3^{2016}.4}\)

P/s : Chắc là vậy