Question

1×5分之1 ＋5×9分之1 ＋9×13 ＋...＋（4n－3）（4n＋1）分之1 的简便算法

Answer 1

1×5分之1 ＋5×9分之1 ＋9×13 ＋...＋（4n－3）（4n＋1）分之1

=(1-1/5)/4+(1/5-1/9)/4+(1/9-1/13)/4+.+[1/(4n-3)-1/(4n+1)]/4

=[1-1/5+1/5-1/9+1/9-1/13+.+1/(4n-3)-1/(4n+1)]/4

=[1-1/(4n+1)]/4

=[4n/(4n+1)]/4

=n/(4n+1)