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2/3 : 5/7 x 5/7 :2/3 +1934 = (2/3 : 2/3)x(5/7 : 5/7) +1934 = 1 x 1 +1934 = 1 +1934 = 1935
=3-2/2*3+4-3/3*4+5-4/4*5+6-5/5*6 =3/2*3-2/2*3+4/3*4-3/3*4+5/4*5-4/4*5+6/5*6-5/5*6 =1/2-1/6 =4/12=1/3
\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)
\(=1-\dfrac{1}{8}=\dfrac{7}{8}\)
(1-1/2)×(1-1/3)×(1-1/4)×(1-1/5)×1-1/6=1/2×2/3×3/4×4/5×5/6=1/6
\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\)
\(=\dfrac{1}{2}-\dfrac{1}{50}=\dfrac{12}{25}\)
Lời giải:
$\frac{1}{5}: \frac{1}{3}\times \frac{1:5}{1:3}+1934$
$=\frac{1}{5}\times 3\times \frac{3}{5}+1934$
$=\frac{3}{5}\times \frac{3}{5}+1934$
$=\frac{9}{25}+1934=1934\frac{9}{25}$