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\(\frac{1+\left[1+2\right]+\left[1+2+3\right]+...+\left[1+2+3+...+100\right]}{100.1+99.2+98.3+...+2.99+1.100}=\frac{1.2:2+2.3:2+3.4:2+...+100.101:2}{100.1+99.2+98.3+...+2.99+1.100}\)
\(=\frac{\frac{1}{2}\left[1.2+2.3+3.4+...+100.101\right]}{100.1+99.2+98.3+...+2.99+1.100}=\frac{\frac{1}{2}\cdot\frac{1}{3}\left[1.2.3-0.1.2+2.3.4-1.2.3+...+100.101.102-99.100.101\right]}{1.100+2.100-1.2+3.100-2.3+...+100.100-99.100}\)
\(=\frac{\frac{1}{6}\cdot100.101.102}{100\left[1+2+3+...+100\right]-\left[1.2+2.3+...+99.100\right]}=\frac{171700}{100\cdot\frac{100.101}{2}-\frac{99.100\cdot101}{3}}\)
\(=\frac{171700}{505000-333300}=\frac{171700}{171700}=1\)
AI THẤY ĐÚNG NHỚ ỦNG HỘ NHÉ
a, x=-5/33
b, x=-30
c, (Nếu dấu của bạn là giá trị tuyệt đối) x=1/3 hoặc x=-1/3
Nếu cần mik giải rõ ràng cho
\(\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{x\left(x+3\right)}=\frac{101}{1504}\)
\(\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{101}{1504}\)
\(\frac{1}{3}\left(\frac{1}{5}-\frac{1}{x+3}\right)=\frac{101}{1504}\)
\(\frac{1}{5}-\frac{1}{x+3}=\frac{101}{1504}:\frac{1}{3}\)
\(\frac{1}{5}-\frac{1}{x+3}=\frac{303}{1504}\)
\(\frac{1}{x+3}=\frac{1}{5}-\frac{303}{1504}\)
\(\frac{1}{x+3}=-\frac{11}{7502}\)
\(x+3=\left(7502.1\right):\left(-11\right)\)
\(x+3=7502:\left(-11\right)\)
\(x+3=-682\)
\(x=-682-3\)
\(x=-385\)
a/ Vì \(x\ge3>-\frac{2}{3}\) nên giá trị biểu thức là :
\(x+\frac{2}{3}+x-3=2x-\frac{7}{3}\)
b/ Vì \(x>2>\frac{4}{3}>-\frac{2}{5}\) nên giá trị biểu thức là :
\(-\left(x+\frac{2}{5}\right)+\left(x-\frac{4}{3}\right)=-\frac{4}{3}-\frac{2}{5}=-\frac{26}{15}\)
Ta có : \(5\cdot\left(\frac{1}{5}+\frac{1}{17}\right)-\left(\frac{2}{5}+\frac{2}{17}+\frac{9}{15}+\frac{12}{68}\right)\)
\(=\) \(5\cdot\frac{1}{5}+5\cdot\frac{1}{17}-\left(\frac{2}{5}+\frac{2}{17}+\frac{3}{5}+\frac{3}{17}\right)\)
\(=\) \(1+\frac{5}{17}-\left[\left(\frac{2}{5}+\frac{3}{5}\right)+\left(\frac{2}{17}+\frac{3}{17}\right)\right]\)
\(=\) \(1+\frac{5}{17}-\left(1+\frac{5}{17}\right)\)
\(=\) \(1+\frac{5}{17}-1-\frac{5}{17}\)
\(=\)\(0\)
Vậy ...
Tk ủng hộ mk nha các bn ❣❣ C.ơn nhiều ^^
( X - 1/2 ) . 5/2 + 1/2 = 7/4
( X - 1/2 ) . 5/2 = 7/4 - 1/2
( X - 1/2 ) . 5/2 = 5/4
X - 1/2 = 5/4 : 5/2
X - 1/2 = 1/2
X = 1/2 + 1/2
X = 1/4
\(\left(x-\frac{1}{2}\right).\frac{5}{2}+\frac{1}{2}=\frac{7}{4}\)
<=>\(\left(x-\frac{1}{2}\right).\frac{5}{2}=\frac{5}{4}\)
<=>\(x-\frac{1}{2}=\frac{5}{4}:\frac{5}{2}\)
<=>\(x-\frac{1}{2}=\frac{1}{2}\)
<=>x=1
\(\frac{x}{2}+\frac{3}{5}.\left(x-2\right)=3\)
\(\frac{x}{2}+\frac{3}{5}x-\frac{6}{5}=3\)
\(\frac{x}{2}+\frac{3x}{5}=\frac{21}{5}\)
\(\frac{11x}{10}=\frac{21}{5}\)
\(11x=42\)
\(x=\frac{42}{11}\)
Ta có: \(\frac{1}{2}x+\frac{3}{5}.\left(x-2\right)=3\)
\(\frac{1}{2}x+\frac{3}{5}x-\frac{6}{5}=3\)
\(\frac{11}{10}x=\frac{21}{5}\)
\(x=\frac{42}{11}\)