Math

Student name : In Sovannarath IB Math SL October, 24th, 2011 Mathematics run Level Portfolio Task Introduction The aim of this internal assessment is to enquire the heart and soul of infinity. In this portfolio task I am going to go over the infinite matrimonymation. Ill check into the sum of the infinite installing 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 lead the above rank of scathe where x = 1 and a = 2. Lets generate Sn is the sum of the commencement exercise (n+1) term of this sequence. Now Ill calculate S0 , S1, S2, S3, S4, S5S10. ( 0?n?10 ) by hire 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 betwixt the likeness 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 lifelike record1 that I used stand out to plot the graph between the relation between Sn and n. Graph 1 essay 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 high than 2. We can set the humanity for Sn which 1?Sn?2. The value of n will...If you postulate to get a adept essay, order it on our website: Orderessay

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