阅读下面短文，从A、B、C、D四个选项中选出最佳选项。

    David is a good student at school, but he is not clean. His face and hands are often dirty. He washes them with water only. He doesn't like to use soap(肥皂). He has an aunt. His aunt comes to see him. She looks at David and says, " David, I know what you ate for breakfast this morning." "What?" David looks at his aunt and asks.

"Eggs," says his aunt. "Your face and mouth tell me that."

    "You are wrong, my dear aunt!" says David. "Not today or yesterday, but the day before yesterday."

一质点做匀加速直线运动，初速度为2m/s，加速度为5m/s²，试求该质点：

小明同学在求1+5¹+5²+5³+5⁴+5⁵+5⁶+5⁷+5⁸+5⁹+5¹⁰的值时，认真思考后发现，从第二个加数起每一个加数都是前一个加数的5倍，于是他想到了下面的一种解题思路．

解：设S=1+5¹+5²+5³+5⁴+5⁵+5⁶+5⁷+5⁸+5⁹+5¹⁰…①

在①式的两边同时都乘以5得：

5S=5¹+5²+5³+5⁴+5⁵+5⁶+5⁷+5⁸+5⁹+5¹⁰+5¹¹…②

②﹣①得：5S﹣S=5¹¹﹣1，即4S=5¹¹﹣1，∴S=$\frac{5^{11}-1}{4}$，得出答案后，爱动脑筋的小明想：如果把“5”换成字母“a”（a≠0且a≠1），能否求出1+a+a²+a³+a⁴+…+a²⁰¹⁴的值？则求出的答案是（　　）