Find the sum of the series.
2+6+18+54+...+2(3^9)

Question

Find the sum of the series.
2+6+18+54+...+2(3^9)

anonymous · Answer

$$\sum_{n=0}^{9}2(3^n)$$

Do you know the formula for sum of geometric series?

anonymous · Answer

thank you but i just figured it out...the only thing i still get confused on is how do you find the n?(number of terms)

anonymous · Answer

How do you find what the n is equal to?

anonymous · Answer

yes i understand that but the question is telling me that the first term is 2 therefore you start at 2 not zero

phi · Answer

The last term is a clue.  It shows 2*3^9
if we use that same pattern on the first term:  2 
we would write it as  2*3^0  (3^0 is 1, so this works)
the second term: 6 we can write as 2*3  or 2*3^1
3rd term is 18, or 2*9  or 2*3^2
so it looks like you have

2* 3^0 + 2* 3^1 + 2*3^2 + ...+ 2*3^9
you can factor a 2 out from each term:
2 ( 3^0+3^1 + 3^2+ ...+3^9)
then use the summation symbol to make the sum look nicer
$$ 2 \sum_{n=0}^9 3^n$$