\(B=\frac{1}{1.2}=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(B=\left(1-\frac{1}{2018}\right)-\left(\frac{1}{2}-\frac{1}{2}\right)-...-\left(\frac{1}{2017}-\frac{1}{2017}\right)\)
\(B=1-\frac{1}{2018}=\frac{2017}{2018}\)
Vậy \(B=\frac{2017}{2018}\)
Cho A= \(\frac{1}{2015}+\frac{2}{2016}+\frac{3}{2017}+...................+\frac{2016}{4030}-2016\) và B= \(\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}+...................+\frac{1}{4030}\) . Chứng minh rằng \(\frac{A}{B}\) là một số nguyên
Cho A= \(\frac{1}{2015}+\frac{2}{2016}+\frac{3}{2017}+...................+\frac{2016}{4030}-2016\) và B= \(\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}+...................+\frac{1}{4030}\) . Chứng minh rằng \(\frac{A}{B}\) là một số nguyên
chứng minh
M=\(\dfrac{3}{1^2\times2^2}+\dfrac{5}{2^2\times3^2}+\dfrac{7}{3^2\times4^2}+.......+\dfrac{19}{9^2\times10^2}< 1\)
Cho: \(A=\frac{1}{2015}+\frac{2}{2016}+\frac{3}{2017}+..............+\frac{2016}{4030}-2016\)
và \(B=\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}+.............+\frac{1}{4030}\)
Chứng minh rằng: \(\frac{A}{B}\) là một số nguyên
\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...-\frac{1}{2016}+\frac{1}{2017}-\frac{1}{2018}\)
\(B=\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\)
Tính \(\left(A^{2017}-B^{2017}\right)^{2018}\)
Tính B\(=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}}{\frac{2016}{1}+\frac{2003}{2}+\frac{2002}{3}+...+\frac{1}{2016}}\)
Tính
A) \(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-1\frac{15}{17}+\frac{2}{3}\)
B) \(\left(-2\right)^3\times\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)
Tìm x
A) \(4\frac{1}{3}:\frac{\chi}{4}=6:0,3\)
B) \(\left(2^3:4\right)\times2^{\left(\chi+1\right)}=64\)
\(A=\frac{2017}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+...+2017}}\)
Cho S = \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\)
P = \(1+\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2018}\)
Chứng minh rằng: \(\left(S-P\right)^{2018}=1\)