PROBLEM 2:
Write center and radius of convergene for the following 3 infinite series in Table below. Give step by step work to get your answers.
HINT 1:(m)!=m(m-1)(m-2) imes dots imes 1.
ex 1: (m+3)!=(m+3)(m+2)(m+1)(m)!
ex 2:(3n)!=3n(3n-1)(3n-2) imes dots imes 1.
ex 3:(3(n+1))!=(4n+4)!=(4n+4)(4n+3)(4n+3)(4n+1)(4n)!
HINT 2: Let B_(m)=((m+1)/(m))^(4m)=(1+(1)/(m))^(4m) then for lim_(m->infty )B_(m)=e^(4)
able[[Infinite Series, able[[Radius of],[Convergence]],center],[sum_(n=0)^(infty ) (2(2n)!n!)/(3^(n)(3n)!)(z-1+i2)^(n),,],[sum_(n=0)^(infty ) ((z-10)/(6+i8))^(2n),,],[Hint: this is the Geometric,,],[series with q=((z-10)/(6+i8))^(2),,],[sum_(n=0)^(infty ) (6(4n+2)!)/(5^(n) imes (2n+2)!(2n)^(2n))z^(n),,]]
PROBLEM 2:
Write center and radius of convergene for the following 3 infinite
series in Table below.Give step by step work to get your answers.
HINT 1: (m)! = m(m - 1)(m - 2) x ...x 1.
ex1:(m+3!=(m+3(m+2(m+1m)!
ex 2: (3n)!= 3n(3n - 1)(3n - 2) x ...x 1.
ex 3:(3(n +1)!=(4n+ 4)!=(4n+4)(4n +3)(4n + 3)(4n+1)(4n)
4m then for lim Bm = e4 m m-0o
m+1
HINT 2: Let Bm
m
Infinite Series
Radius of Convergence
center
2(2n)!n! > z-1+ i2)n 3n(3n)! n=0
-102n 8+9 n=0
Hint: this is the Geometric z-102 series with q = 8+9
8
6 (4n + 2)!
n=0
