(9x7+8x9-15x9):(1+3+5+7+ ....+17+19)
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[ 9x7+8x9-15x9] : [ 2+3+4+5+.....+18+19+20]
= 63 + 72 - 135 : [1+2+3+4+5+....+18+19+20]
= ( 135 - 135 ) : [ 1+2+3+4+5+....+18+19+20]
= 0 : [ 1+2+3+4+5+...+18+19+20]
= 0
b1
a) \(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
\(=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=\dfrac{1}{5}-\dfrac{1}{10}\)
\(=\dfrac{2}{10}-\dfrac{1}{10}\)
\(=\dfrac{1}{10}\)
b) \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\)
\(=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=\dfrac{1}{1}-\dfrac{1}{100}\)
\(=\dfrac{99}{100}\)
c) \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\)
\(=\dfrac{1}{3}-\dfrac{1}{11}\)
\(=\dfrac{8}{33}\)
d) \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\)
\(=\dfrac{1}{3}-\dfrac{1}{101}\)
\(=\dfrac{98}{303}\)
a: =2/3(4/9+5/9)=2/3
d: =15/16(9/5-4/5)=15/16
e: =13/25(5-3-1)=13/25
\(9\times7+8\times9-15\times9.\\ =9\times\left(7+8-15\right)=9\times0=0.\)
\(\Rightarrow\left(9\times7+8\times9-15\times9\right):\left(1+3+5+7+...+17+19\right).\\ =0:\left(1+3+5+7+...+17+19\right).\\ =0.\)
\(=\left(15\cdot9-15\cdot9\right):\left(1+3+...+17+19\right)=0\)