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\(A=\frac{3}{2.1.2.5}+\frac{3}{2.2.3.5}+\frac{3}{2.3.4.5}+\frac{3}{2.4.5.5}+...+\frac{3}{2.99.100.5}\)
\(A=\frac{3}{2.5}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\right)\)
Đặt biểu thức trong ngoặc đơn là B
\(B=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{100-99}{99.100}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(B=1-\frac{1}{100}=\frac{99}{100}\)
\(A=\frac{3}{2.5}.B=\frac{3.99}{2.5.100}=\frac{297}{1000}\)
\(1-\frac{3}{2.10}-\frac{3}{4.15}-\frac{3}{6.20}-\frac{3}{8.25}-...-\frac{3}{198.500}\)
\(=1-\left(\frac{3}{2.10}+\frac{3}{4.15}+\frac{3}{6.20}+...+\frac{3}{198.500}\right)\)
\(=1-\frac{3}{2.5}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
\(=1-\frac{3}{10}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=1-\frac{3}{10}.\left(1-\frac{1}{100}\right)\)
\(=1-\frac{3}{10}.\frac{99}{100}\)
\(=1-\frac{297}{1000}\)
\(=\frac{703}{1000}\)
P/s : Không biết đúng hông nha, làm đại
\(A=1-\left(\frac{3}{2.10}+\frac{3}{4.15}+\frac{3}{6.20}+....+\frac{3}{198.500}\right)\)
\(=1-\frac{3}{2.5}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
\(=1-\frac{3}{25}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=1-\frac{3}{25}\left(1-\frac{1}{100}\right)\)
\(=1-\frac{3.99}{25.100}=\frac{703}{1000}\)
B = 1 - 3/2×10 - 3/4×15 - 3/6×20 - ... - 3/198×500
B = 1 - (3/2×10 + 3/4×15 + 3/6×20 + ... + 3/198×500)
B = 1 - 3/2×5 × (1/1×2 + 1/2×3 + 1/3×4 + ... + 1/99×100)
B = 1 - 3/10 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100)
B = 1 - 3/10 × (1 - 1/100)
B = 1 - 3/10 × 99/100
B = 1 - 297/1000
B = 703/1000
\(\frac{x}{5}=\frac23\)
\(x\) = \(\frac23\times5\)
\(x=\frac{10}{3}\)
Vậy \(x=\frac{10}{3}\)
\(\frac{x}{3}-\frac12=\frac15\)
\(\frac{x}{3}\) = \(\frac15\) + \(\frac12\)
\(\frac{x}{3}\) = \(\frac{2}{10}+\frac{5}{10}\)
\(\frac{x}{3}=\frac{7}{10}\)
\(x=\frac{7}{10}\times3\)
\(x=\frac{21}{10}\)
Vậy \(x=\frac{21}{10}\)
\(\frac{x}{5}+\frac12=\frac{6}{10}\)
\(\frac{x}{5}=\frac{6}{10}-\frac12\)
\(\frac{x}{5}=\frac{6}{10}-\frac{5}{10}\)
\(\frac{x}{5}=\frac{1}{10}\)
\(x=\frac{1}{10}\times5\)
\(x=\frac12\)
Vậy \(x=\frac12\)
\(\frac{x+3}{15}\) = \(\frac13\)
\(x+3=\frac13\times15\)
\(x+3=5\)
\(x=5-3\)
\(x=2\)
Vậy \(x=2\)
a) = 3/3 x ( -24/54 +45/54 ) : 7/12
= 1 x 21/54 x 12/7
= 18/27
( hiện tại mik chỉ lm đc thế này thui. thông cảm nk )
S = \(\frac12\times\frac13\) + \(\frac13\times\frac14\) + \(\frac14\times\frac15\) + \(\frac15\times\frac16\) + \(\frac17\times\frac18\) + \(\frac18\times\frac19\)
S = \(\frac12\) - \(\frac13\) + \(\frac13\) - \(\frac14\) + \(\frac14\) - \(\frac15\) + \(\frac15\) - \(\frac16\) + \(\frac17\) - \(\frac18\) + \(\frac18\) - \(\frac19\)
S = \(\frac12\) - \(\frac19\)
S = \(\frac{9}{18}-\frac{2}{18}\)
S = \(\frac{7}{18}\)