Как решить 1/15+1/35+1/63+1/99+1/143+1/195 ?

Question

Как решить 1/15+1/35+1/63+1/99+1/143+1/195 ?

Comments

1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)+1/(13*15)=

Answer 1

1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13

)+1/(13*15)=1/2( 1/3 -1/5) +1/2(1/5-1/7) +
+1/2(1/7-1/9) +1/2(1/9-1/11)+1/2(1/1-13)++ 1/2(1/13-1/15) =1/2(1/3 -1/15) =2/15