Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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
9 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
9 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

 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free