SOLUTION: The function is written in long form to describe a visual branching problem-- a center star with three points, each of those branching to three points, etc. For n=1, total poin

Question 54783: The function is written in long form to describe a visual branching problem-- a center star with three points, each of those branching to three points, etc.
For n=1, total points (x) = 1
For n=2, total points (x) = 1 + 3
For n=3, x = 1 + 3 + 3 squared
For n=4, x = 1 +3 + 3square + 3 cubed
So the last number in the sequence is always 3 with an exponent of (n-1)
Short of brute force with a calculatorm how would I calculate x for n=100?
How would I write the formula?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For n=4, x = 1 +3 + 3square + 3 cubed
So the last number in the sequence is always 3 with an exponent of (n-1)
Short of brute force with a calculatorm how would I calculate x for n=100?
How would I write the formula?
--------
Notice this pattern:
(1-x^2)/(1-x)=1+x
(1-x^3)/(1-x)=1+x+x^2
(1-x^4)/(1-x)=1+x+x^2+x^3
...
...
(1-x^101)/(1-x)= 1+x+x^2+....+x^100
---------
So, let x=3
1+3+3^2+3^3+...+3^100= (1-3^101)/(1-3)
(1-3^101)/(1-3)= -1.54613256x10^48/-2=7.73066281x10^47
The formula is the last line with the x's.
Cheers,
Stan H.

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