# Summation problem......

• Oct 19th 2010, 08:17 PM
Arka
Summation problem......
How do I find the summation of 1+3+9+........+n without assuming any summation formula?
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• Oct 19th 2010, 08:38 PM
Educated
As I can see from the sequence, I see that it is a geometric sequence.

You can use the formula: $S_n=\dfrac{ar^n - a}{r - 1}$

Where:
a = the first term
r = common ratio, which in this case is 3
n = nth term that it goes to
• Oct 19th 2010, 11:27 PM
Arka
Quote:

Originally Posted by Educated
As I can see from the sequence, I see that it is a geometric sequence.

You can use the formula: $S_n=\dfrac{ar^n - a}{r - 1}$

Where:
a = the first term
r = common ratio, which in this case is 3
n = nth term that it goes to

But I said without assuming any summation formula ....
• Oct 20th 2010, 01:10 AM
Educated
Oh, I thought you meant without the sigma notation $\sum$.

In that case, the only way that I can think of is by just adding them up manually.
• Oct 20th 2010, 01:15 AM
mr fantastic
Quote:

Originally Posted by Arka
But I said without assuming any summation formula ....

What you do is reproduce the working that leads to the general formula for this particular question, that is, derive the formula from first principles for this particular question.
• Oct 20th 2010, 01:29 AM
Arka
Thanks a lot..............Mr. Fantastic....