Given an equation of an exponential line how would I get the sum of all previous whole numbers in that line down to 0.
For example.
With the equation:
$y = 100 \times 1.3 ^x$
How would I create another equation to get the sum of all previous values given x?
for example, an equation that would get me this sum column.
|---x---|100 * 1.3 ^ x|--sum--| ------------------------------ |---0---|-----100-----|--100--| |---1---|-----130-----|--230--| |---2---|-----169-----|--399--| |---3---|-----220-----|--619--|
I've searched and found triangle numbers (x2 + x)/2 which is almost what I'm searching for but have failed to find a way to implement this using an equation.
Best Answer
So you want to compute the sum
$$\sum_{k=0}^n 100 a^k$$
For $a=1.3$
Then, for any $a\neq1$,
$$\sum_{k=0}^n 100 a^k=100\sum_{k=0}^n a^k=100\frac{a^{n+1}-1}{a-1}$$
Have a look at: https://en.wikipedia.org/wiki/Geometric_series