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\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}.\left(\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right)=\frac{1}{2}.\frac{22}{45}=\frac{11}{45}\)
= \(\frac{1x1x1}{1x2x4}x\frac{2.2.1}{1.1.2.2}=\frac{1}{8}.1=\frac{1}{8}\)
=1X2X3/1X2X3X4X2= 1/8 =3X2X2X2X5/3X2X2X5X2= 1/1
=1/8X1/1=1/8
\(\frac{2}{1\times2}+\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{9\times10}\)
=\(2\times\frac{1}{1\times2}+2\times\frac{1}{2\times3}+2\times\frac{1}{3\times4}+...+2\times\frac{1}{9\times10}\)
=\(2\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{9\times10}\right)\)
=\(2\times\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
=\(2\times\left(\frac{1}{1}-\frac{1}{10}\right)=2\times\left(\frac{10}{10}-\frac{1}{10}\right)=2\times\frac{9}{10}\)
=\(\frac{9}{5}\)
=2-1+1-\(\frac{2}{3}\)+\(\frac{2}{3}\)-\(\frac{1}{2}\)+...+\(\frac{2}{9}\)-\(\frac{1}{5}\)
=2-\(\frac{1}{5}\)
=\(\frac{10}{5}\)-\(\frac{1}{5}\)
=\(\frac{9}{5}\).
**** mình nha mấy bạn.
( 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 +1/5.6 ) x 10 - x = 0
= ( 1- 1/2 +1/2 -1/3 +1/3 - 1/4 + 1/4 - 1/5 +1/5 -1/6 ) x 10 - x = 0
= ( 1 - 1/6 ) x 10 - x = 0
= 5/6 x 10 - x =0
= 25/3 - x =0
x = 25/3 - 0
x = 25/3
\(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\right)\times10-x=0\)
\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\times10-x=0\)
\(\left(\frac{1}{1}-\frac{1}{6}\right)\times10-x=0\)
\(\frac{5}{6}\times10-x=0\)
\(\frac{25}{3}-x=0\)
x =\(\frac{25}{3}-0=\frac{25}{3}\)
B =\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=\dfrac{2}{3}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=\dfrac{7}{9}-\dfrac{1}{10}=\dfrac{61}{90}\)
\(\frac{1}{8}=12,5\%\) ; \(\frac{1}{16}=6,25\%\) ; \(\frac{1}{2}=50\%\) ; \(\frac{1}{4}=25\%\)
Thay vào trên mà tính.
= \(1+\left(\frac{3\left(1x2+2x4x2\right)}{3\left(5+5x3x25\right)}+1\right)-\left(1+\frac{18}{54}\right)-1\) = \(\frac{18}{380}-\frac{18}{54}\)
\(\frac{1.2.6.4.6.4.5.2}{2.3.6.8.6.2.2.2.8.10}=\frac{1}{96}\)
