(-2/3+1và 1/4-1/6)-24/10
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ta có
\(1+\frac{1}{3}+\frac{1}{6}+...+\frac{2}{x\left(x+1\right)}\) \(=\)\(1+2\)\(\left(\frac{1}{2}-\frac{1}{3}\right)+2\left(\frac{1}{3}-\frac{1}{4}\right)+...+2\left(\frac{1}{x}-\frac{1}{x+1}\right)\)\(=2-\frac{2}{x+1}\)
Nên ta có
\(2-\frac{2}{x+1}=1+\frac{1989}{1991}\Leftrightarrow\frac{2}{x+1}=\frac{2}{1991}\Leftrightarrow x=1990\)
\(1\frac{1}{2}\times1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times...1\frac{1}{9}+2005.\)
\(=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times...\times\frac{10}{9}+2005\)
\(=\frac{10}{2}+2005=5+2005=2010\)
.
A) x/y-3/8=1 x/y-3/8=1/2 B)4/9:x/y=1 4/9:x/y=2/3
x/y=1+3/8 x/y=1/2+3/8 x/y=4/9:1 x/y=4/9:2/3
x/y=8/8+3/8 x/y=4/8+3/8 x/y=4/9 x/y=2/3
x/y=11/8 x/y=7/8
( - \(\dfrac{2}{3}\) + 1\(\dfrac{1}{4}\) - \(\dfrac{1}{6}\)) - \(\dfrac{24}{10}\)
= - \(\dfrac{2}{3}\) + \(\dfrac{5}{4}\) - \(\dfrac{1}{6}\) - \(\dfrac{24}{10}\)
= \(\dfrac{-40}{60}\) + \(\dfrac{25}{60}\) - \(\dfrac{10}{60}\) - \(\dfrac{144}{60}\)
= \(-\dfrac{169}{60}\)