Question

请问这题计算的规律怎么找?

(1+1/1乘3)乘(1+1/2乘4)乘(1+1/3乘5)乘(1+1/4乘6)乘……乘(1+1/98乘100)=

Answer 1

化简一下
（4/3）（9/8）（16/15）.....
=（2*2/1*3）（3*3/2*4）（4*4/3*5）.....（98*98/97*99）（99*99/98/100）
写在纸上，把可以约掉的约掉
=（2/1）*（99/100）
=99/50

Answer 2

(1+1/n(n+2))
=(1+1/((n+1)^2-1))
=(n+1)^2/(n(n+2))
=n/(n-1) * n/(n+1)

(1+1/1乘3)乘(1+1/2乘4)乘(1+1/3乘5)乘(1+1/4乘6)乘……乘(1+1/98乘100)
=(2/1 * 2/3)*(3/2 * 3/4)*……*(99/98 * 99/100)
=(2/1 * 3/2 * 4/3 *……*99/98) * (2/3 * 3/4 *……*99/100)
=99 * 2/100
=1.98