Method NO. 1 : Upseting Method, The sum of a geometric sequence

22Dec07

Asume that we want to calculate
S_n = \sum_{\substack{0 \leq k \leq n}}ax^k
Of course, S_n +ax^{n+1} = ax^0 + \sum_{\substack{0 \leq k \leq n}}ax^{k+1}
But the sum on the right side is equal to x \sum_{\substack{0 \leq k \leq n}}ax^k = xS_n Therefore S_n + ax^{n+1} = a + xS_n and so, S_n = \sum_{\substack{0 \leq k \leq n}}ax^k = \frac{a-ax^{n+1}}{1-x}



No Responses Yet to “Method NO. 1 : Upseting Method, The sum of a geometric sequence”

  1. Leave a Comment

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: