2x3:6x1000+10x12=
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\(=\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{10}-\dfrac{1}{10}-\dfrac{1}{12}+\dfrac{1}{12}+\dfrac{1}{13}\)
=1/2+1/13
=15/26
a) \(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{5}-\frac{1}{10}\)
\(=\frac{1}{10}\)
b) \(\frac{2}{10.12}+\frac{2}{12.14}+\frac{2}{14.16}+...+\frac{2}{998.1000}\)
\(=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+\frac{1}{14}-\frac{1}{16}+...+\frac{1}{998}-\frac{1}{1000}\)
\(=\frac{1}{10}-\frac{1}{1000}\)
\(=\frac{99}{1000}\)
c) \(\frac{4}{1.2}+\frac{4}{2.3}+\frac{4}{3.4}+...+\frac{4}{69.90}\)
\(=4.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{89.90}\right)\)
\(=4.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{89}-\frac{1}{90}\right)\)
\(=4.\left(1-\frac{1}{90}\right)\)
\(=4.\frac{89}{90}\)
\(=\frac{178}{45}\)
_Chúc bạn học tốt_
Ta có :
\(\left|5x-6\right|+120^2=0\)
\(\left|5x-6\right|+14400=0\)
\(\left|5x-6\right|=-14400\)
Ta có x thuộc rỗng do GTTĐ luôn có kết quả lớn hơn 0
⟹2/3B= 2/10.12+3/12.14+...+3/48.50
⟹2/3B=1/10-1/12+1/12-1/14+...+1/48-1/50
⟹2/3B=1/10-1/50
⟹2.3B=4/50
⟹B=4/50:2/3
⟹B=4/50.2/3
⟹B=8/150
`M=4/(10xx12)+4/(12xx14)+4/(14xx16)+...+4/(96xx98)`
`M=2xx(2/(10xx12)+2/(12xx14)+2/(14xx16)+...+2/(96xx98))`
`M=2xx(1/10-1/12+1/12-1/14+1/14-1/16+...+1/96-1/98)`
`M=2xx(1/10-1/98)`
`M=2xx22/245`
`M=44/245`
= 3 x ( \(\frac{1}{10x12}+\frac{1}{12x14}+\frac{1}{14x16}+\frac{1}{96x98}\))
= 3 x (\(\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+\frac{1}{14}-\frac{1}{16}+......+\frac{1}{96}-\frac{1}{98}\))
= 3 x ( \(\frac{1}{10}-\frac{1}{98}\))
= 3 x \(\frac{22}{245}\)
= \(\frac{66}{245}\)
\(\frac{3}{10.12}+\frac{3}{12.14}+\frac{3}{14.16}+...+\frac{3}{96.98}=\frac{3}{2}\left(\frac{2}{10.12}+\frac{2}{12.14}+\frac{2}{14.16}+...+\frac{2}{96.98}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+\frac{1}{14}-\frac{1}{16}+...+\frac{1}{96}-\frac{1}{98}\right)\)
\(=\frac{3}{2}\left(\frac{1}{10}-\frac{1}{98}\right)=\frac{3}{2}.\frac{22}{245}=\frac{33}{245}\)
2x3:6x1000+10x12
=1000+120
=1120
1120