- (i) 1 (D) (ii) (− 1 )n+^1 n (D) (iii) n(. 9 )n−^1 (C)
(iv)(− 1 )n+^1
√
n(C) (v) n^3 (. 95 )n−^1 (C) (vi)2 n− 1
2 n(D)(vii) (− 1 )n+^12 n− 1
2 n(D) (viii)2 n− 1
2 n^2(D)19.(i) |x|< 1 (ii) |x|<^12 (iii) allx (iv) |x|< 1
(v) C for|x|<1, D for|x|>1, D forx=± 1- 1 + 3 x+^32 x^2 +···, 4 , |x|<^12
- (i) 2x−
4
3x^3 Allx (ii) 1+x^2 +x^4
2!+··· Allx(iii) 1+ 3 x+ 9 x^2 + 27 x^3 + 81 x^4 +···|x|<1
3(iv) 2x− 2 x^2 +8
3x^3 − 4 x^4 +···−1
2<x<1
2
(v) x+1
3x^3 +··· x^2 <π^2
4(You are not expected to derive this condition,but it is obvious from the graph of tanx!)
(vi) 1− 2 x+ 3 x^2 − 4 x^3 + 5 x^4 +···|x|< 1