Summations with Fractional Indices (Future Value)

Scenario A: Assume you can invest $40,000 each year starting at age 23 and ending at age $n$, earning a 7% return. Assume you leave the money invested until age 60.
Scenario B: Assume you can invest $40,000 each year starting at age $n+1$ and ending at age 60, earning a 7% return. Assume you leave the money invested until age 60.
For what age $n$ would the account value at age 60 of Scenario A equal Scenario B?

I have set up the following sums to represent this problem:
$$sum_{k=23}^{n}40000(1.07)^{60-k}=sum_{k=n+1}^{60}40000(1.07)^{60-k}$$

How do you solve for $n$? You can just try all the numbers and see where they come out closest, but somehow Wolfram Alpha comes up with $n=31.1558$. A fractional number doesn’t make since in the context of sum indices, so I have no idea how it’s getting this.

Is there some continuous representation of the sum that it’s using? How do you calculate $31.1558$?