Question

1/3+1/15+1/35+1/63+1/99+1/143等于几

1/3+1/15+1/35+1/63+1/99+1/143等于几

Answer 1

1/3+1/15+1/35+1/63+1/99+1/143
=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)+1/(11x13)
=(1/2)x[(1-1/3)+(1/3-1/5)+.....+(1/11-1/13)]
=(1/2)x(1-1/13)
=6/13

Answer 2

1/3+1/15+1/35+1/63+1/99+1/143
＝5/15+1/15+1/35+1/63+1/99+1/143
＝6/15+1/35+1/63+1/99+1/143
＝2/5+1/35+1/63+1/99+1/143
＝14/35+1/35+1/63+1/99+1/143
＝15/35+1/63+1/99+1/143
＝3/7+1/63+1/99+1/143
＝27/63+1/63+1/99+1/143
＝28/63+1/99+1/143
＝4/9+1/99+1/143
＝44/99+1/99+1/143
＝45/99+1/143
＝5/11+1/143
＝65/143+1/143
＝66/143
＝6/13

Answer 3

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 4

找规律的题，