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chú ý:1/2=1/2^1
BIỂU THỨC A có:2018-1+1=2018 số hạng
A=(1/2^1+1/2^2018)+(1/2^2+1/2^2017)+...+(1/2^1008+1/2^1011)+(1/2^1009+1/2^1010)
A= 1 + 1 + ... + 1 + 1 (có 2018:2=1009 số 1)
A= 1009
MÌNH GIẢI ĐÊN ĐÂY PHÀN YÊU CẦU CHỨNG MINH BẠN GHI RÕ HỘ MÌNH RỒI MÌNH SẼ GIÚP BẠN TIẾP
a, \(5-\left(\frac{a}{b}+\frac{1}{2}\right)=2\frac{1}{3}\) => \(\frac{a}{b}+\frac{1}{2}=5-2\frac{1}{3}\) => \(\frac{a}{b}+\frac{1}{2}=\frac{8}{3}\) => \(\frac{a}{b}=\frac{8}{3}-\frac{1}{2}\) => \(\frac{a}{b}=\frac{13}{6}\)
b, \((\frac{3}{4}+2\frac{1}{2}):\frac{3}{5-3}=\left(\frac{3}{4}+\frac{5}{4}\right):\frac{3}{5}-1=\frac{9}{4}:\frac{-2}{5}=\frac{-45}{8}\)
a, 5-(\(\frac{a}{b}\)+\(\frac{1}{2}\))=2\(\frac{1}{3}\)
<=>5-\(\frac{a}{b}-\frac{1}{2}\)=\(\frac{7}{3}\)
<=>\(\frac{a}{b}=5-\frac{1}{2}-\frac{7}{3}\)
<=>\(\frac{a}{b}=\frac{13}{6}\)
b,(\(\frac{3}{4}\)+2\(\frac{1}{2}\)):\(\frac{3}{5}\)-3
=(\(\frac{3}{4}\)+\(\frac{5}{2}\)).\(\frac{5}{3}\)-3
=\(\frac{23}{4}\).\(\frac{5}{3}\)-3
=\(\frac{115}{12}\)-3
=\(\frac{115-36}{12}\)
=\(\frac{79}{12}\)
a) Ta có ; \(\frac{x}{5}=\frac{2}{3}\Rightarrow3.x=2.5\)\(\)
\(\Rightarrow3.x=10\)
\(\Rightarrow x=10:3\)
\(\Rightarrow x=\frac{10}{3}\)
Vậy \(x=\frac{10}{3}\)
b)\(\frac{x}{3}-\frac{1}{2}=\frac{1}{5}\)\(\Leftrightarrow\frac{10x}{30}-\frac{15}{30}=\frac{6}{30}\)
\(\Rightarrow10x-15=6\)
\(\Rightarrow10x=6+15\)
\(\Rightarrow10x=21\)
\(\Rightarrow x=21:10\)
\(\Rightarrow x=\frac{21}{10}\)
Vậy\(x=\frac{21}{10}\)
a. x/5 = 2/3
x. 3 = 5. 2
x. 3 = 10
x = 10 : 3
x = 10/3. Vậy x = 10/3
b. x/3 - 1/2 = 1/5
x/3 = 1/5 + 1/2
x/3 = 7/10
x.10 = 3. 7
x. 10 = 21
x = 21 : 10
x = 21/10
Vậy x = 21/10
B = (1 + 1/2)(1 + 1/3)(1 + 1/4) ...(1 + 1/100)
= \(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{101}{100}\)
= \(\frac{3.4.5....101}{2.3.4...100}=\frac{101}{2}\)
C = \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{1000}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{999}{1000}\)
\(=\frac{1.2.3...999}{2.3.4....1000}=\frac{1}{1000}\)
`a)25/(x+1)-1 1/6=-1/3-0,5`
`=>25/(x+1)=-1/3-1/2+1+1/6`
`=>25/(x+1)=1/3`
`=>75=x+1`
`=>x=74`
Vậy `x=74`
`b)(2x+25 3/5)^2-9/25=0`
`=>(2x+128/5)=9/25`
`**2x+128/5=3/5`
`=>2x=-125/5=-25`
`=>x=-25/2`
`**2x+128/5=-3/5`
`=>2x=-131/5`
`=>x=-131/10`
\(=\frac{1}{2}\frac{2}{3}\frac{3}{4}\frac{4}{5}\frac{5}{6}\frac{6}{7}\frac{7}{8}\frac{8}{9}....\frac{2002}{2003}\frac{2003}{2004}\)
\(=\frac{1}{2004}\)
Ta có :
\(B=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right).....\left(1-\frac{1}{2003}\right)\left(1-\frac{1}{2004}\right)\)
\(B=\frac{1}{2}.\frac{2}{3}.....\frac{2002}{2003}.\frac{2003}{2004}\)
\(B=\frac{1.2.....2002.2003}{2.3.....2003.2004}\)
\(B=\frac{1}{2004}\)
Vậy \(B=\frac{1}{2004}\)
Chúc bạn học tốt ~
B= 1/2.2/3.3/4......2002/2003.2003/2004=1/2004