- #1
mateomy
- 307
- 0
Im practicing inductions on my own and I am getting stuck on one in particular...
[tex]
S_n = \frac{3(3^n-1)}{2} for a_n = 3^n
[/tex]
I know that
[tex]
S_1 = 3
[/tex]
when you plug 1 into the equation, because it is the first term in the sequence
Therefore,
[tex]
S_1 = a_1 = 3
[/tex]
I need to prove then
[tex]
S_{n+1} = \frac{3(3^{n+1} -1)}{2}
[/tex]
I know that I need to add S*sub(n) to a*sub(n+1)
so doing that I get
[tex]
\frac{3(3^n - 1) + 2(3^{n+1})}{2}
[/tex]
I don't understand how to get it to match with what I am supposed to prove.
Did I go in the right steps?
[tex]
S_n = \frac{3(3^n-1)}{2} for a_n = 3^n
[/tex]
I know that
[tex]
S_1 = 3
[/tex]
when you plug 1 into the equation, because it is the first term in the sequence
Therefore,
[tex]
S_1 = a_1 = 3
[/tex]
I need to prove then
[tex]
S_{n+1} = \frac{3(3^{n+1} -1)}{2}
[/tex]
I know that I need to add S*sub(n) to a*sub(n+1)
so doing that I get
[tex]
\frac{3(3^n - 1) + 2(3^{n+1})}{2}
[/tex]
I don't understand how to get it to match with what I am supposed to prove.
Did I go in the right steps?