Remark
When you take the limit of [tex] \lim_{ 0} \frac{sin(x)}{x} [/tex] the odd result you get is 1. Later on you will be able to use calculus to show this. For now just take limits of sin(x)/x and make sure you are feeding radians into your calculator.
Now the only question is what is this thing doing?
If a is a constant in [tex] \lim_{0 \frac{sin(ax)}{x} [/tex] then the result = a.
So that's basically all you need to know to solve your problem.
Series
Each term in the series will be
a*(sin(ax)/x) = a * [sin(ax)/x] * 1 = a * a = a^2
The series will look like this.
1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 There is a way of summing this using n notation, but you could just as easily just add the results.
The formula for this series (if you want a sum) is n*(n+1)*(2n+1) / 6
n = 10
Sum = 10*(11)(21)/6
Sum = 385
Does adding it by hand bring up 385?
