Question

1/3+1/15+1/35+1/63+1/99+1/143的简便运算

Answer 1

1/3=1/2*(1/1 -1/3)1/15=1/2*(1/3 -1/5)1/35=1/2*(1/5 -1/7)1/63=1/2*(1/7 -1/9)1/99=1/2*(1/9 -1/11)61/143=1/2*(1/11 -1/13)所以结果=1/2*(1 -1/13)=6/13

Answer 2

1/3+1/15+1/35+1/63+1/99+1/143
=1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11+13)
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13
=1-1/13
=12/13

Answer 3

1/2*(1-1/3)+1/2*(1/3-1/5)+…+1/2*(1/11-1/13)=1/2*(1-1/13)=6/13够明白了吧？

Answer 4

1/3=(1/1-1/3)/21/15=(1/3-1/5)/21/35=(1/5-1/7)/2...1/143=(1/11-1/13)/21/3+1/15+1/35+1/63+1/99+1/143=(1/1-1/13)/2=6/13

Answer 5

1/3+1/15+1/35+1/63+1/99+1/143
=1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13
=(1/2)(1-1/3)+(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)(1/11-1/13)
=(1/2)(1-1/13)
=6/13