\(\frac{1}{5}+\frac{4}{5}:5=\)
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\(S=\frac{5}{3.13}+\frac{5}{13.23}+.....+\frac{5}{83.93}\)
\(2S=\frac{2.5}{3.13}+\frac{2.5}{13.23}+....+\frac{2.5}{83.93}\)
\(2S=\frac{10}{3.13}+\frac{10}{13.23}+.....+\frac{10}{83.93}\)
\(2S=\frac{1}{3}-\frac{1}{13}+\frac{1}{13}-\frac{1}{23}+....+\frac{1}{83}-\frac{1}{93}\)
\(2S=\frac{1}{3}-\frac{1}{93}=\frac{30}{93}\)
\(S=\frac{30}{93}.\frac{1}{2}=\frac{15}{93}\)
Sửa đề:
\(S=\frac{5}{3.13}+\frac{5}{13.23}+.....+\frac{5}{83.93}\)
\(S=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{13}+\frac{1}{13}-\frac{1}{23}+....+\frac{1}{83}-\frac{1}{93}\right)\)
\(S=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{93}\right)\)
\(S=\frac{1}{2}.\left(\frac{31}{93}-\frac{1}{93}\right)\)
\(S=\frac{1}{2}.\frac{10}{31}\)
\(S=\frac{5}{31}\)
Bạn làm theo cách này nhé:
\(\frac{7}{5}\div\frac{4}{5}=\frac{7}{4}\)(5 ở trên tử và 5 ở dưới mẫu triệt tiêu còn 1)
Ta có: \(\frac{7}{4}>1>\frac{2005}{2006}\Rightarrow\frac{7}{4}\div\frac{4}{5}>\frac{2005}{2006}\)
Ta có
\(S=\left(\frac{1}{3}+\frac{1}{4}\right)+\left(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}\right)+\left(\frac{1}{9}+\frac{1}{10}+...+\frac{1}{16}\right)+\left(\frac{1}{17}+\frac{1}{18}+...+\frac{1}{32}\right)\)
\(S>\frac{1}{4}.2+\frac{1}{8}.4+\frac{1}{16}.8+\frac{1}{32}.16=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{1}{2}.4=2\)
Vậy S>2
a,<=>\(\frac{\left(2x+1\right)^2}{4}\)+\(\frac{2\left(2x-1\right)^2}{4}\)≥\(\frac{12\left(x+5\right)^2}{4}\)
<=>4x2+4x+1+2(4x2-4x+1)≥12(x2+10x+25)
<=>4x2+4x+1+8x2-8x+2≥12x2+120x+300
<=>4x2+4x+1+8x2-8x+2-12x2-120x-300≥0
<=>-124x-297≥0
<=>124x+297≤0
<=>124x≤-297
<=>x≤\(\frac{-297}{124}\)
b, Tương tự câu a
c, |5−3x|=2+x
TH1: 5-3x=2+x
<=> -3x - x = 2 - 5
<=> -4x = -3
<=> x = 3/4
TH2: 5-3x = -2 - x
<=> -3x + x = -2 - 5
<=> -2x = -7
<=> x = 7/2
\(B=\frac{5}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+....+\frac{1}{2014}-\frac{1}{2017}\right)\)
\(B=\frac{5}{3}.\left(1-\frac{1}{2017}\right)\)
\(B=\frac{5}{3}.\frac{2016}{2017}=\frac{10080}{6051}\)
\(B=\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{2014.2017}\)
\(3M=5\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{2014.2017}\right)\)
\(3M=5\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{2014}-\frac{1}{2017}\right)\)
\(3M=5\left(1-\frac{1}{2017}\right)\)
\(3M=5.\frac{2016}{2017}\)
\(3M=\frac{10080}{2017}\)
\(\Rightarrow M=\frac{3360}{2017}\)
ĐKXĐ: \(x\notin\left\{0;\frac{3}{2}\right\}\)
Ta có: \(\frac{1}{2x-3}-\frac{3}{x\left(2x-3\right)}=\frac{5}{x}\)
\(\Leftrightarrow\frac{x}{x\left(2x-3\right)}-\frac{3}{x\left(2x-3\right)}=\frac{5\left(2x-3\right)}{x\left(2x-3\right)}\)
Suy ra: \(x-3=10x-15\)
\(\Leftrightarrow x-3-10x+15=0\)
\(\Leftrightarrow-9x+12=0\)
\(\Leftrightarrow-9x=-12\)
hay \(x=\frac{4}{3}\)(tm)
Vậy: \(S=\left\{\frac{4}{3}\right\}\)
\(\frac{1}{5}\)+\(\frac{4}{5}\): 5=\(\frac{5}{5}\): 5=1:5=\(\frac{1}{5}\)
Đ/S \(\frac{1}{5}\)
\(\frac{1}{5}+\frac{4}{5}:5=\frac{1}{5}+\frac{4}{5}.\frac{1}{5}=\frac{1}{5}+\frac{4}{25}=\frac{5}{25}+\frac{4}{25}=\frac{9}{25}\).
Chúc cậu hok tốt!
#Dũng