一道数学题,用等比数列的求和知识：

题目

一道数学题,用等比数列的求和知识：
A frog jumps 0.5m.It then jumps 0.1m and on each subsequent jump travels 0.2m of the previous distance.Find the total distance through which the frog jumps.
一只青蛙跳了0.5米,然后跳了0.1米,接下来每次跳的距离是之前距离的0.2倍,求青蛙总共跳的距离

答案

等比数列求和公式：Sn=a1(1-q^n)/(1-q),a1=0.5,q=0.2.
这道题是求当n->无穷的时候Sn趋近的值,将数据带入Sn=0.5(1-0.2^n)/(1-0.2),当n->正无穷时,0.2^n->0,所以就是0.5*1/(1-0.2)=5/8米.