First one
120 - 80 +160/3 -320 / 9 +.....
r = (-80 / 120) = -2/3
The sum is
First term 120 120
_________ = _______ = ______ = 120 (3/5) = 72
1 - r 1 - (-2/3) (5/3)
2 .
(a) Ratio Test = a (n + 1) / a (n) =
[2(n + 1 )! ] / [ 2^(2n + 1) ] 2 (n + 1)! 2^(2n) n
_____________________ = ________ * _________ = _____ = r
2n! / 2^(2n) 2n! 2^(2n + 1) 2
(b) This series will diverge as n grows larger and larger
3 (a) Not sure about this one
3(b) Expansion is
(3x^5)^4 - 4(3x^5)^3 * [(1/9)y]^3 + 6(3x^5)^2 * [ ( 1/9)y^3]^2 - 4 (3x^5)* [(1/9)y]^3 + [ (1/9)y^3]^4 =
81x^20 - 12x^15y^3 + (2/3)x^10 y^6 - (4/243)x^5 y^9 + (1/6561)y^12
+128399 
