*** Please show all the step detail, neatly and well organizaed *** 1. Describe
ID: 2982757 • Letter: #
Question
*** Please show all the step detail, neatly and well organizaed ***
1. Describe the difference between the series and sequence.
2. Watch the embedded video or use the link below and post your answer on the discussion board.
(Note: Please follow the link (if there is not link , please copy and paste)
then Explain me detail, neatly please !! )
a) Explain What is radius of convergence for a series?
http://www.youtube.com/watch?v=QQBtF7_KJrE
b) What is wrong with the Math on the video you just watched?
Explanation / Answer
i am answering the questions without seeing the video , as normally we do not watch these videos as they may be infected...
1.sequence is just a set of numbers written as per some rule ..like...
1 , 2 ,3 ,4 ,5 ,.....,n,.............
it is a just a number denoted by its n th. term ..here ..n th. term = n
2. series is the sum of the terms in the sequence ..that is continuing from the above example .....series is ..1+2+3+4+5+.....+n+......
that is the essential difference ...
next we talk of convergence ..
a sequence is convergent if its n th. term tends to a finite real number as n tends to infinity ..
for ex..the sequence .....1/1 , 1/2 , 1/3 , 1/4 , ......, 1/ n ,........is convergent since its n th. term ...1 / n ......tends to zero as n tends to infinity ...
a series is convergent if its sum up to n terms tends to finite real value as n tends to infinity ......
for ex.. the above sequence written as series ...
.1/1 + 1/2 + 1/3 + , 1/4 + ......+ 1/ n +.....is divergent as it tends to infinity as n tends to infinity....
as we can infer from above ..a sequence may converge but not the series...
but if a series is convergent then obviously its terms forming a sequence is convergent ...
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radius of convergence is used for power series where there will be some power of x in the n th . term ..like say ....
1+x/1!+ x^2/2!+x^3/3!+......+x^n/n!+.......
so here whether tghe limit of the sum tends to a real finite value or not depends on the value of x .. the range of those values of x for which the series is convergent is called the
the interval or convergence or radius of convergence ..
suppose a given series like ....1+x+x^2+x^3+....+x^n+...is convergent if |x|<1 ...
that is in the interval (-1,1)...excluding -1 and + 1..
we call radius of convergence is 1 excluding the boundary values of -1 and +1
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the 3 rd. part , i can not respond without seeing the video ..
i am sorry i can not do it for reasons explained ..
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