Question

计算:1乘以4分之一加4乘以7分之一加7乘以10分之一加10乘以13分之一加···加21乘以24等

计算:1乘以4分之一加4乘以7分之一加7乘以10分之一加10乘以13分之一加···加21乘以24等于多少

Answer 1

注意到1/{n(n+3)} = 1/3{1/n-1/(n+1)}

1乘以4分之一加4乘以7分之一加7乘以10分之一加10乘以13分之一加···加21乘以24
= 1/3×{1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+.....+1/21-1/24}
= 1/3×{1-1/24}
= 1/3×23/24
= 23/8
= 2又7/8

Answer 2

1/(1x4)+1/(4X7)+1/(7X10)+......+1/(22X25)
=(1/3)X(1-1/4+1/4-1/7+1/7-1/10+......+1/22-1/25)
=(1/3)X(1-1/25)
=(1/3)X(24/25)
=8/25