1.

Matchthe followingcolumnsandchoosethe correctanswer. {:(,"Column I",,,"Column II"),((A), (1 - x) ^(-n),,(1),(x)/(x + 1)),((B),(1-x) ^(-n),,(2), 1- nx + (n(n+1))/(2!) x ^ 2 -... if |x| lt 1),((C), If x gt 1", then " 1 +(1)/(x) +(1)/(x^2) + ..." is",,(3), 1 + nx + (n(n+1))/(2!) x ^ 2+ ... if |x| lt 1),((D), if|x| gt 1", then" 1 - (2 )/(x^2) + (3)/(x^4)- (4)/(x^6) + ...,,(4),(x)/(x-1)),(,,,(5), (x^4)/((x^2 + 1)^2)),(,,,(6),(x^4)/((x^2 -1)^2)):}

Answer»

`{:(""(A),(B),(C ),(D)),(1, 3, 4,5 ):}`
`{:(""(A), (B), (C ), (D)),(2, 3,4, 5):}`
`{:(""(A), (B), (C ), (D)),(3, 2, 4, 5):}`
`{:(""(A), (B), (C ), (D)),(2, 3, 1, 5):}`

Solution :(a)`(1 -x ) ^(-n )= 1+nx+ (n(n + 1 ))/(2 !)x ^ 2+…, if|x|lt1`
(b) `(1 + x ) ^ (-n )= 1- nx+ (n (n + 1 ))/(2! )x ^2 - …, if |x|lt1`
(c )`1 +(1)/(x)+ (1)/(x^ 2 )+ … = (1)/(1 - (1)/(x)) = (x ) /(x - 1 ) , ifx gt1`
` [ becausea+ ar+ ar ^ 2 + ...=(a )/( 1 - r ), if |r|lt1 ]`
(d)`1 -(2)/(x^ 2 )+ (3)/ (x ^ 4)- (4)/(x ^ 6)+ ... = ( 1+ (1)/(x^ 2 ))^ (-2) `
` = ((x^ 2 )/(1 + x ^ 2)) ^ 2 `
`= (x ^4)/((1 + x ^ 2 )^ 2 ) , if |x| gt 1`


Discussion

No Comment Found

Related InterviewSolutions