Math

Student name : In Sovannarath IB Math SL October, 24th, 2011 Mathematics sit Level Portfolio Task Introduction The aim of this internal sound judgment is to enquire the pump of infinity. In this portfolio task I am going to investigate the infinite tallymation. Ill investigate the sum of the infinite instalment tn , where : t0 = 1, t1 = (xlna)1 , t2 = (xlna)22×1 , t3 = (xlna)33×2×1 tn = (xlna)nn! .. set-back of all I am going to consider the supra sequence of boundarys where x = 1 and a = 2. allows consecrate Sn is the sum of the first (n+1) term of this sequence. Now Ill calculate S0 , S1, S2, S3, S4, S5S10. ( 0?n?10 ) by utilise GDC (TI-83) S0 = t0 = 1 S1 = S0 + t1 = 1 + ln21 = 1 + 0.693147 = 1.693147 S2 = S1 + t2 = 1.693147 + (ln2)22×1 = 1.693147 + 0.240226 = 1.933373 S3 = S2 + t3 = 1.933373 + (ln2)33! = 1.933373 + 0.055504 = 1.988877 S4 = S3 + t4 = 1.988877 + (ln2)44! = 1.988877 + 0.009618 = 1.998495 S5 = S4 + t5 = 1. 998495 + (ln2)55!= 1.998495 + 0.001333 = 1.999828 S6 = S5 + t6 = 1.999828 + (ln2)66! = 1.999828 + 0.000154 = 1.999982 S7 = S6 + t7 = 1.999982 + (ln2)77! = 1.999982 + 0.000015 = 1.999997 S8 = S7 + t8 = 1.999997 + (ln2)88! = 1.999997 + 0.000001 = 1.999998 S9 = S8 + t9 = 1.999998 + (ln2)99! = 1.999998 + 0.0000001 = 1.9999981 S10 = S9 + t10 = 1.9999981 + (ln2)1010! = 1.9999981 + 0.

000000007 = 1.999998107 Here is the table1 between the relation back between Sn and n that I used by GDC n Sn 0| 1| 1| 1.693147| 2| 1.933373| 3| 1.988877| 4| 1.998495| 5| 1.999828| 6| 1.999982| 7| 1 .999997| 8| 1.999998| 9| 1.9999981| 10! | 1.999998107| This is the graphical record1 that I used excel to plot the graph between the relation between Sn and n. Graph 1 show the sum of infinite sequence when x=1 and a=2. When n=0 , the sum is 1 and as n increase Sn increase but it cannot go higher than 2. We can set the domain for Sn which 1?Sn?2. The value of n will...If you want to get a full essay, order it on our website: BestEssayCheap.com

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