Question

1/3+1/15+1/35+1/63+1/99+1/143=？怎样简便计算

Answer 1

1/3+1/15+1/35+1/63+1/99+1/143

分解 15=3x5, 35=5x7, 63=7x9, 99=9x11, 143=11x13

=1/3+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)+1/(11x13)

partial fraction

=1/3+(1/2)[(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)]

一前一后互相抵消

=1/3 +1/6 -1/26

=(26+13-3)/78

=36/78

=18/39

=6/13

Answer 2

1/3+1/15+1/35+1/63+1/99+1/143

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

=1/2*(1-1/13)

=1/2*12/13

=6/13

Answer 3

拆分。
原式=1/2*（1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13）
=1/2*(1-1/13)
=6/13

Answer 4

解:
1/3+1/15+1/35+1/63+1/99+1/143
=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*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)
=1/2*(1-1/13)
=1/2*12/13
=6/13