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a)summation notation symbol (n=1 to infinity) of ((n+1)(x^n))/((n^(2n))
b)summation notation symbol (n=0 to infinity) of ((4^(n+1) x^(2n))/(n+3)
c) summation notation symbol ( n=1 to infinity) of ((-1)^(n+1) .1.3.5....(2n-1)(x^n))/(2.4.6.... 2^n)

2007-10-03 03:59:59 · 1 answers · asked by Anonymous in Science & Mathematics Mathematics

1 answers

Take abs val and apply ratio test
Ia_n+1 / a_nI = IxI* (n+2)/(n+1)* (n^2n/(n+1)^2n+2)
(n+2)/(n+1)==>1 and [(n/(n+1)]^2n==>1/e^2 and1/(n+1)^2==>0
so the limit is 0 and the series is absolutely convergent for all x
2) ratio test = 4*x^2*(n+3)/(n+4) ===> 4x^2
so 4x^2<1 -1/2 at extremes
a_n = 4*4^n/4^n *1/(n+3)= 4/(n+3) is of the same class as 1/n divergent
3) Now you can do it

2007-10-03 08:48:26 · answer #1 · answered by santmann2002 7 · 0 0

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