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10/5.7+10/7.9+...+10/61.63
=2.(5/5.7+5/7.9+.....+5/61.63)
5/5.7=5/5-5/7
=5.(5/5.7+5/7.9+....+5/61.63)
=5.(5/5-5/7+5/7-5/9+...+5/61-5/63)
=5.(5/5-5/63)
=5.(315/315-25/315)
=5.290/315
=1450/315=290/63
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\(M=\frac{3}{5.7}+\frac{3}{7.9}+....+\frac{3}{61.63}\)
\(2M=2.\left(\frac{3}{5.7}+\frac{3}{7.9}+.....+\frac{3}{61.63}\right)\)
\(2M=3.\left(\frac{2}{5.7}+\frac{2}{7.9}+.....+\frac{2}{61.63}\right)\)
\(2M=3.\left(\frac{1}{5}-\frac{1}{63}\right)\)
\(2M=\frac{3.58}{315}=\frac{58}{105}\)
\(M=\frac{58}{105}.\frac{1}{2}=\frac{29}{105}\)
Ta có thể vt gọn thành :
M = \(\frac{3}{2}\).( \(\frac{1}{5}\)\(-\)\(\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\)... \(+\frac{1}{61}-\frac{1}{63}\))
M = \(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{63}\right)\)
M = \(\frac{3}{2}.\frac{58}{315}\)
M = \(\frac{29}{105}\)
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`a) ((-14).15)/(21.(-10))`
`=(-7.3.5.3)/(7.3.(-2).5)`
`=3/2`
`b) ((-7).12)/((-16).(-14))`
`=(-7.3.2.2)/(-2.2.2.(-7).2)`
`=(-3)/4`
`c) ((-11).(-5))/(15.22) `
`=(-11.(-5))/(3.5.11.2)`
`=1/6`
`d) ((-10).(-18))/((-6).25.7)`
`=(-5.2.-2.3.3)/(-2.3.5.5.7)`
`=6/35`
`e) (5.7-7.9)/(7.2+6.7)`
`=(7.(5-9))/(7.(2+6))`
`=-4/8`
`=-1/2`
`f) (11.9-22.3)/(33.2)`
`=(33.(3-2))/(33.2)`
`=1/2`
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A=(1-1/2^2)(1-1/3^2).....(1-1/10^2)
=(1-1/4)(1-1/9)....(1-1/100)
=3/4.8/9......99/100=1.3.2.4.....9.11/(2.3.....10)^2=1.2.3.....11/(3.....10).10=2.11/10=22/10=11/5
B=1/1.3+1/3.5+1/5.7+1/7.9
= 2.(1/1.3+1/3.5+1/5.7+1/7.9).1/2=(1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9).1/2=(1/1-1/9).1/2=8/9.1/2=4/9
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=3.2/1.3.2+3.2/3.5.2+...+3.2/49.51
=3/2.(2/1.3+2/3.5+2/5.7+...+2/49.51)
=3/2.(1-1/3+1/3-1/5+...+1/49-1/51)
=3/2.(1-1/51)
=3/2.50/51
=25/17
CHÚC BẠN HỌC GIỎI
K MÌNH NHÉ
A=3/2(2/3.5+2/5.7+...+2/61.63)
=3/2(1/3-1/5+1/5-1/7+...+1/61-1/63)= 3/2(1/3-1/63)=3/2 x 20/63=10/21
Đs: 10/21