1/1.2+1/2.3+...+1/2009.2010
=1-1/2+1/2-1/3+...+1/2009-1/2010
=1-1/2010
=2009/2010
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Tính giá trị của biểu thức:
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}\)
\(B=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(C=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+....+\frac{1}{990}\)
a)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}\)
b)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)
c)\(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{2012.2015}\)
K=\(\frac{4}{2.4}\)+\(\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
F=\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
I=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}\)
Tính tổng các phân số sau:
\(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) + \(\frac{1}{3.4}\) + ... +\(\frac{1}{2009.2010}\)
\(\left(1-\frac{1}{1.2}\right).\left(1-\frac{1}{2.3}\right)....\left(1-\frac{1}{2009.2010}\right)\)Tính
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{199.200}\)
($\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + ... + $\frac{1}{2011. 2012}$ ) x = 2011
\(A=-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-...-\frac{1}{\left(n-1\right).n}\)
chứng minh:\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}< 1\)