Question

 

a ) tìm :   \(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)

b )  tìm x : 1 - ( \(1-\left(5\frac{3}{8}+x-7\frac{5}{24}\right):\left(-16\frac{2}{3}\right)=0\)

giúp mình nha!

Answer 1

a) \(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{195}\)

= \(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\)

= \(\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\right)\)

= \(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)

= \(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{15}\right)\)

= \(\frac{1}{2}.\frac{4}{15}\)

= \(\frac{2}{15}\)