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1.)The number of real negative terms in the binomial expansion of (1+ix) ^4n-2, n belongs to N and x>0 is???Please give the solution with detailed explanation. Thank You!!

1.)The number of real negative terms in the binomial expansion of (1+ix) ^4n-2, n belongs to N and x>0 is???Please give the solution with detailed explanation. 


Thank You!!

Grade:11

2 Answers

Ashwin Muralidharan IIT Madras
290 Points
12 years ago

Hi Chaitanya,

 

ir will be negative whenever r = 2,6,10....

So all the terms where power of ix is 2,6,10,.....4n-2 will be negative.

So there will be "n" terms that are negative.

 

Hope it helps.

Wish you all the best.

 

Regards,

Ashwin (IIT Madaras).

Swapnil Saxena
102 Points
12 years ago

The binomial expansion of (1+ix)^4n-2 is

4n-2C0 (i)^0 +4n-2C1(i)^1 +4n-2C2(i)^2+4n-2C3(i)^3+4n-2C4(i)^4+.....+4n-2C4n-1(i)^4n-1+4n-2C4n-2(i)^4n-2

Term is real when exponent of i is divisible by 2 and negative when it not divisible by 4. Then exponent  is 2,6,10,...,4n-2

Therefore the no of such terms is n

 

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