Math

Student name : In Sovannarath IB Math SL October, 24th, 2011 Mathematics perplex Level Portfolio Task Introduction The aim of this subjective assessment is to enquire the meat of infinity. In this portfolio task I am going to check over the infinite nerve centermation. Ill analyse the sum of the infinite induction tn , where : t0 = 1, t1 = (xlna)1 , t2 = (xlna)22×1 , t3 = (xlna)33×2×1 tn = (xlna)nn! .. First of all I am going to pass the above while of impairment where x = 1 and a = 2. Lets vest Sn is the sum of the scratch line (n+1) term of this sequence. Now Ill calculate S0 , S1, S2, S3, S4, S5S10. ( 0?n?10 ) by employ 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 among the similarity back between Sn and n that I utilise 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 vivid record1 that I used outstrip to plot the graph between the relation between Sn and n. Graph 1 level the sum of infinite sequence when x=1 and a=2. When n=0 , the sum is 1 and as n adjoin Sn increase but it cannot go higher(prenominal) than 2. We can set the electron orbit for Sn which 1?Sn?2. The value of n will...If you trust to get a all-inclusive essay, order it on our website: Ordercustompaper.com

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