3分之1加15分之1加35分之1加63分之1加99分之1这道数学题怎么做

3分之1加15分之1加35分之1加63分之1加99分之1这道数学题怎么做

解：
1/3+1/15+1/35+1/63+1/99
=1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
=½(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=½(1- 1/11)
=5/11

总结：
本题是拆项法的典型题目。
知识拓展：
本题项数较少，项数较多时，再按以上方法，各项都写出，就太繁琐了，下面推导一下n为任意正整数时的表达式：
1/(1×3)+1/(3×5)+...+1/[(2n-1)(2n+1)]
=½[1-1/3+1/3-1/5+...+1/(2n-1)-1/(2n+1)]
=½[1- 1/(2n+1)]
=n/(2n+1)

答案是11分之5
=1/3+1/3*5+1/5*7+1/7*9+1/9*11
=1/3+1/2(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/3+1/2(1/3-1/11)
=1/3+1/2*8/33
=5/11

1/3+1/15+1/35+1/63+1/99
=1/3+1/2(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/3+1/2(1/3-1/11)
=1/3+1/6-1/22
=1/2-1/22
=5/11