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\(B=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{10}\)
\(B=\frac{1}{3}-\frac{1}{10}\)
\(B=\frac{7}{30}\)
- \(A=\frac{1}{3.4}-\frac{1}{4.5}-\frac{1}{5.6}-\frac{1}{6.7}-\frac{1}{7.8}-\frac{1}{8.9}-\frac{1}{9.10}\)
A= 1/3 + 1/4-1/4+1/5-1/5+1/6-1/6+1/7-1/7+1/8-1/8+1/9-1/9+1/10
A=1/3+1/10
A=13/30
a,\(A=\frac{1}{3.4}-\frac{1}{4.5}-\frac{1}{5.6}-....-\frac{1}{8.9}-\frac{1}{9.10}\)
\(=\frac{1}{12}-\left(\frac{1}{4.5}+\frac{1}{5.6}+....+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(=\frac{1}{12}-\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(=\frac{1}{12}-\frac{1}{4}+\frac{1}{10}=\frac{5}{60}-\frac{15}{60}+\frac{6}{60}=\frac{-1}{15}\)
Vậy \(A=\frac{-1}{15}\)
\(B=\frac{1}{3.4}-\frac{1}{4.5}-\frac{1}{5.6}-\frac{1}{6.7}-\frac{1}{7.8}-\frac{1}{8.9}-\frac{1}{9.10}\)
\(\Rightarrow B=\frac{1}{3.4}-\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(\Rightarrow B=\frac{1}{12}-\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(\Rightarrow B=\frac{1}{3}-\frac{1}{4}-\left(\frac{1}{4}-\frac{1}{10}\right)\)
\(\Rightarrow B=\frac{1}{12}-\frac{6}{40}\)
\(\Rightarrow B=\frac{-1}{15}\)
\(\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-\frac{1}{6.7}-\frac{1}{5.6}-\frac{1}{4.5}-\frac{1}{3.4}-\frac{1}{2.3}-\frac{1}{1.2}\)
\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)+\frac{1}{9.10}\)
\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)+\frac{1}{90}\)
\(=-\left(1-\frac{1}{10}\right)+\frac{1}{90}\)
\(=-\frac{9}{10}+\frac{1}{90}\)
= ...
bn tự tính nha!
bạn tìm 1 số để nhân cả tử cả mẫu ra để tử ra 1 so chung nha rồi tách thôi
Gọi 3 phân số đó là \(\frac{a}{x},\frac{b}{y},\frac{c}{z}\)
Ta có các tử tỉ lệ với 3;4;5=>a:b:c=3:4:5=>\(\frac{a}{3}=\frac{b}{4}=\frac{c}{5}\)
Đặt \(\frac{a}{3}=\frac{b}{4}=\frac{c}{5}=k\)
=>\(\hept{\begin{cases}a=3k\\b=4k\\c=5k\end{cases}}\)
Lại có các mẫu tỉ lệ với 5,1,2=>x:y:z=5:1:2=>\(\frac{x}{5}=\frac{y}{1}=\frac{z}{2}\)
Đặt \(\frac{x}{5}=\frac{y}{1}=\frac{z}{2}=h\)
=> \(\hept{\begin{cases}x=5h\\y=h\\z=2h\end{cases}}\)
Ta có tổng 3 phân số là \(\frac{213}{70}\)
=> \(\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=\frac{213}{70}\)
(=) \(\frac{3k}{5h}+\frac{4k}{h}+\frac{5k}{2h}=\frac{213}{70}\)
(=) \(\frac{k}{h}.\left(\frac{3}{5}+4+\frac{5}{2}\right)=\frac{213}{70}\)
(=) \(\frac{k}{h}=\frac{3}{7}\)
=> \(\hept{\begin{cases}\frac{a}{x}=\frac{9}{35}\\\frac{b}{y}=\frac{12}{7}\\\frac{c}{z}=\frac{15}{14}\end{cases}}\)
bài 3
Ta có \(\frac{3a-2b}{5}=\frac{2c-5a}{3}=\frac{5b-3c}{2}\)
= \(\frac{15a-10b}{25}=\frac{6c-15a}{9}=\frac{10b-6a}{4}\)
=\(\frac{15a-10b+6c-15a+10b-6a}{25+9+4}=0\)
=> \(\hept{\begin{cases}3a-2b=0\\2c-5a=0\\5b-3c=0\end{cases}\left(=\right)\hept{\begin{cases}3a=2b\\2c=5a\\5b=3c\end{cases}\left(=\right)\hept{\begin{cases}\frac{a}{2}=\frac{b}{3}\\\frac{c}{5}=\frac{a}{2}\\\frac{b}{3}=\frac{c}{5}\end{cases}}}}\)
=> \(\frac{a}{2}=\frac{b}{3}=\frac{c}{5}=\frac{a+b+c}{2+3+5}=\frac{-50}{10}=-5\)
=> \(\hept{\begin{cases}a=-10\\b=-15\\c=-25\end{cases}}\)
b)\(\frac{-15.8+10.7}{5.6+20.3}=\frac{-15.8+10.7}{5.2.3+5.4.3}=\frac{-90+70}{5.3.\left(2+4\right)}=\frac{-20}{90}=-\frac{2}{9}\)
\(\frac{2^4.5^2.7}{2^3.5.7^2.11}=\frac{2.5.1}{1.1.7.11}=\frac{10}{77}\)
MSC:77.9=693
\(\frac{-2}{9}=\frac{-2.693}{9.693}=\frac{-1386}{6237}\)
\(\frac{10}{77}=\frac{10.693}{77.693}=\frac{6930}{53361}\)
a) \(\frac{4.5+4.11}{8.7+4.3}=\frac{4.\left(5+11\right)}{56+12}=\frac{4.16}{68}=\frac{64}{68}=\frac{16}{17}.\)
Mình chỉ làm câu a) thôi nhé.
Chúc bạn học tốt!