Infinite Summation

IB Mathematics SL I IA Lab: Infinite Summation

Kristen Rodríguez Mr. Zivkovich May 2010

1

When one considers the concept of infinite summation, there are many observable patterns between the exponent on the numerator and both the result and the sum of the series. This investigation aims to explore this concept of infinite summation and finally arrive at a general statement to determine the sum of the infinite sequence tn. The analysis will also discuss the scope and limitations of the general statement and test the validity by using various values of a and x. Conclusions will be supported by mathematical examples. The following function will be considered, where x and a remain constant throughout the entirety of the sequence and …show more content…

Sn tends to ½, which happens to be 2-1.

7) 1, T9 (3,-2) S10 =      Ž  Ž   =  Ž      § 1/9 Ž       Ž        



 

   

               

Unlike the pattern observed in example 6, Sn tends to 1/9, which happens to be 3-2.

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8) 1, T9 ( ½ ,-3) S10 =      Ž  Ž   =  Ž      §8 Ž       Ž        



 

   

               

Like the patterns observed in examples 6 and 7, Sn tends to ax, which is 8 in this case. An interesting pattern can be observed from the above three examples of 6-8. Sn tends to ax.

9-11) To further facilitate the exploration of Tn, a will remain constant to test the pattern observed above while x will vary positively. A=2 T9 (2; 2, 4, 6) 9)


T9 (2, 2)    Ž  Ž   =  Ž      §4

 

   

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