tính nhanh 2/3*5+2/5*7+/7*9+....2/13*15
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a: \(\frac{-1}{9}\cdot\frac{-3}{5}+\frac{5}{-6}\cdot\frac{-3}{5}-\frac72\cdot\frac35\)
\(=\frac19\cdot\frac35+\frac56\cdot\frac35-\frac72\cdot\frac35\)
\(=\frac35\left(\frac19+\frac56-\frac72\right)\)
\(=\frac35\left(\frac{2}{18}+\frac{15}{18}-\frac{63}{18}\right)=\frac35\cdot\frac{-46}{18}=\frac35\cdot\frac{-23}{9}=\frac{-23}{3\cdot5}=-\frac{23}{15}\)
b: Sửa đề: \(-\frac37\cdot\frac{15}{13}-\frac37\cdot\frac{11}{13}-\frac37\)
\(=-\frac37\left(\frac{15}{13}+\frac{11}{13}\right)-\frac37\)
\(=-\frac37\cdot2-\frac37=-\frac37\cdot3=-\frac97\)
1^3-3^5-(-3^5)+1^64-2^9-1^36+1^15
=1+(-3^5+3^5)+1-2^9-1+1
=2-2^9
=-510
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
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{13\cdot15}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\)
\(=\frac{1}{3}-\frac{1}{15}\)
\(=\frac{4}{15}\)
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{13\cdot15}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{13}+\frac{1}{15}-\frac{1}{15}\)
\(=\frac{1}{3}-\frac{1}{15}=\frac{4}{15}\)