Question

篮球落地弹起的路程问题一个篮球从60英尺的高度落地,然后弹起,每次弹起的高度是上一次的2/3.求这颗破球第n次落地时一共

Answer 1

a1=60,a2=60*4/3=120*2/3,a3=60*2/3*2/3*2=60*4/3*2/3=120*(2/3)^2,...,

an=120*(2/3)^(n-1)

a1+a2+...+an=60+120[2/3+...+(2/3)^(n-1)]

=60+120*2/3[1+2/3+...+(2/3)^(n-2)]

=60+80[1-(2/3)^(n-1)]/(1-2/3)

=60+240[1-(2/3)^(n-1)]