Cool Series

There is a nice trick to solve this quick: $\frac{5}{6}-\frac{7}{12}+\frac{9}{20}-\frac{11}{30}+\frac{13}{42}-\frac{15}{56}=$

$= \frac{5}{2}-\frac{5}{3}-\frac{7}{3}+\frac{7}{4}+\frac{9}{4}-\frac{9}{5}-\frac{11}{5}+\frac{11}{6}+\frac{13}{6}-\frac{13}{7}-\frac{15}{7}+\frac{15}{8} =$

$= \frac{5}{2}-4+4-4+4-4+\frac{15}{8}=\frac{3}{8}$

5/6-7/12=1/4(by taking lcm of denominators 6 & 12) 9/20-11/30=1/12(" "20 & 30 and simplifying it) 13/42-15/56=1/24(" "42 & 56) After this u will get 1/4+1/12+1/24 Now taking the lcm of 4,12,24 we get the lcm as 24 then 6+2+1/24=9/24 and by simplifying we get 3/8 :)

Take first two term you will get 1/4 then 3rd and 4th you will get 1/12 and then last two terms you will get 1/24. Now add all these three terms you will get 3/8

Partial fractions XD