Question

一个有关根据规律求解的题已知1/(n-1)n=(1/n-1)-(1/n) x/2+x/6+x/12+.+x/(n-1)n

Answer 1

x/2+x/6+x/12+.+x/(n-1)n

=x*[1/(2-1)2+1/(3-1)3+1/(4-1)4+.1/(n-1)n]

=x*[1/(2-1)-1/2+1/(3-1)-1/3 +1/(4-1)-1/4+.+1/(n-1)-(1/n) ]

=x*[1-1/2+1/2-1/3+1/3-1/4+.1/(n-1)-(1/n) ]

=x*[1-(1/n) ]

=x*(n-1)/n

x*(n-1)/n