Tính \(\dfrac{P}{A}\)biết :
P=\(\dfrac{2013}{2}+\dfrac{2013}{3}+\dfrac{2013}{4}+...+\dfrac{2013}{2014}\)
A = \(\dfrac{2013}{1}+\dfrac{2012}{2}+\dfrac{2011}{1}+....+\dfrac{1}{2013}\)
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 \(1\dfrac{2013}{2014}\)
\(\dfrac{x+1}{2014}+\dfrac{x+2}{2013}=...+\dfrac{x+1007}{1008}=\dfrac{x+1008}{1007}+\dfrac{x+1009}{1006}+...+\dfrac{x+2014}{1}\)
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=\(\dfrac{18}{5^{2012}}+\dfrac{12}{5^{2013}}\)
1) Tìm 2 số nguyên tố x, y sao cho: \(x^2-6y^2=1\)
2) Cho \(B=1.2.3...2012.\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}\right)\)
CMR: B chia hết cho 2013
Chứng tỏ A<1 biết :
A=\(\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+...+\dfrac{2013}{2014!}\)
Tính:
a, A = 1+2-3-4+5+6-7-8 +........+2013+2014
b, B = (1+\(\dfrac{1}{2}\) ) . ( 1+\(\dfrac{1}{3}\) ) . ( 1+\(\dfrac{1}{4}\) ) ....... (1+\(\dfrac{1}{2015}\))
So sánh
\(\dfrac{2011}{2013}+\dfrac{2013}{2015}+\dfrac{2015}{2017}+\dfrac{2017}{2011}\) và 4
tính tổng
A= \(\dfrac{1}{1.6}+\dfrac{1}{2.9}+\dfrac{1}{3.12}+...+\dfrac{1}{670.2017}\)
BT3: Tìm x, biết
3) \(\dfrac{3}{4}.x-\dfrac{5}{3}.x=\dfrac{7}{12}\)
4) \(x-\dfrac{1}{7}=\) \(\dfrac{\dfrac{4}{2011}-\dfrac{4}{2013}+\dfrac{4}{99}}{\dfrac{5}{2011}-\dfrac{5}{2013}+\dfrac{5}{99}}+\dfrac{1}{2}\)
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