A= 1+2-3-4+5+6-7-8+...+2013+2014
A=(1+2-3-4)+(5+6-7-8)+.....+(2013+2014)
A=(-4)+(-4)+...+(-4)+4027
A=(-4).503+4027
A=-2012+4027
A=2015
B=\(\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{2016}{2015}\)
B=\(\dfrac{3.4.5.6.....2016}{2.3.4.5.....2015}=\dfrac{2016}{2}=1008\)
tính giá trị biểu thức sau
A= -1 -2 +3 +4 -5 -6 +7 +8-9-10+11+12 -...........-2013-2014+2015+2016
B= [\(\dfrac{1}{2}\) -1 ] : [\(\dfrac{1}{3}\) -1] : ...................: [\(\dfrac{1}{99}\) -1} : [\(\dfrac{1}{100}\) -1]
Cho A = \(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{4026}\)
B = \(1+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{4025}\)
So sánh \(\dfrac{A}{B}\)với \(1\dfrac{2013}{2014}\)
cho A=\(\dfrac{1}{5}+\dfrac{1}{5^2}+\dfrac{1}{5^3}+...+\dfrac{1}{5^{2014}}+\dfrac{1}{5^{2015}}\)
So sánh A với\(\dfrac{1}{4}\)
a) A = \(\left(\dfrac{1}{1009}+\dfrac{1}{1010}+...+\dfrac{1}{2015}+\dfrac{1}{2016}\right):\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)
b) B = \(\dfrac{5x^2+3y^2}{10x^2-3y^2}\) biết \(\dfrac{x}{3}=\dfrac{y}{5}\)
Tính \(\dfrac{P}{A}\)biết :
P=\(\dfrac{2013}{2}+\dfrac{2013}{3}+\dfrac{2013}{4}+...+\dfrac{2013}{2014}\)
A = \(\dfrac{2013}{1}+\dfrac{2012}{2}+\dfrac{2011}{1}+....+\dfrac{1}{2013}\)
1.Thực hiện phép tính:
a, \(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2016}+\dfrac{1}{2017}\)
b, 2016+\(\dfrac{2015}{2}+\dfrac{2014}{3}+...+\dfrac{2}{2015}+\dfrac{1}{2016}\)
2.a. Tìm các số tự nhiên x, y. sao cho (2x+1)(y-5)=12
b.Tìm số tự nhiên sao cho 4n-5 chia hết cho 2n-1
Chứng minh: \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{2015^2}+\dfrac{1}{2015}\)
Cho biểu thức: A=\(\dfrac{2}{n-1}\left(n\in Z\right).\)Tìm tất cả các giá trị nguyên của n để A là số nguyên.
Không quy đồng mẫu hãy so sánh a và B biết; A=\(\dfrac{12}{5^{2012}}+\dfrac{18}{5^{2013}}\); B=\(\dfrac{18}{5^{2012}}+\dfrac{12}{5^{2013}}\)
Chứng tỏ A<1 biết :
A=\(\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+...+\dfrac{2013}{2014!}\)
a)x=\(\dfrac{1}{4}+\dfrac{2}{13}\)
b)\(\dfrac{x}{3}=\dfrac{2}{3}+\dfrac{-1}{7}\)
c)\(\dfrac{-8}{3}+\dfrac{-1}{3}\le x\le\dfrac{-2}{7}+\dfrac{-5}{7}\)
d)\(\dfrac{-5}{6}+\dfrac{8}{3}\dfrac{29}{-x}\le x\le\dfrac{-1}{2}+2+\dfrac{5}{2}\)