单愿你能看懂。
Rigorous proof by: gyro
Let \int denote integral, x denote time(year), N(x) denote the number of people at age x. Each year there are -dN/dx=-N' people die at age x. The total number of people die in a year is -\int N'dx
The average life span=\int N'xdx/\int N' dx
The average death rate is -\int N'dx/\int N dx
Integration by part,
\int N'xdx=-\int N dx
So life span x death rate = 1
This conclusion holds regardless of the variation of the death rate with age.