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}

Possibly related posts: (automatically generated)


Filed under: Mathematics, Methods   |  Leave a Comment
Tags: , , , ,

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

Feed for this Entry Trackback Address
  1. No Comments Yet

Leave a Reply