Home
Class 12
MATHS
If (1 + x)^(n) = C(0) + C(1) x C(2) x^(2...

If `(1 + x)^(n) = C_(0) + C_(1) x C_(2) x^(2) +…+ C_(n) x^(n)`, then
the sum `C_(0) + (C_(0)+C_(1))+…+(C_(0) +C_(1) +…+C_(n -1))` is equal to

A

`n . 2^(n)`

B

`n . 2^(n-1)`

C

`n . 2^(n-2)`

D

`n. 2^(n-3)`

Text Solution

Verified by Experts

The correct Answer is:
b
Promotional Banner

Topper's Solved these Questions

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos
  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos
  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise For Session 3|10 Videos
  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|23 Videos
  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

Similar Questions

Explore conceptually related problems

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3)x^(3) + …+ C_(n) x^(n) , then C_(0) - (C_(0) - C_(1)) + (C_(0) + C_(1) + C_(2))- (C_(0) + C_(1) + C_(2)+ C_(3)) + ...+ (-1)^(n-1) (C_0) + C_(1) + C_(2) + ...+ C_(n-1)) , when n is even integer is

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) +… + C_(n) x^(n) , prove that C_(0) + 2C_(1) + 3C_(2) + …+ (n+1)C_(n) = (n+2)2^(n-1) .

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + …+ C_(n) x^(n) , then for n odd, C_(1)^(2) + C_(3)^(2) + C_(5)^(2) +....+ C_(n)^(2) is equal to

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that C_(0) C_(n) - C_(1) C_(n-1) + C_(2) C_(n-2) - …+ (-1)^(n) C_(n) C_(0) = 0 or (-1)^(n//2) (n!)/((n//2)!(n//2)!) , according as n is odd or even .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that C_(0)^(2) - C_(1)^(2) + C_(2)^(2) -…+ (-1)^(n) *C_(n)^(2)= 0 or (-1)^(n//2) * (n!)/((n//2)! (n//2)!) , according as n is odd or even Also , evaluate C_(0)^(2) + C_(1)^(2) + C_(2)^(2) - ...+ (-1)^(n) *C_(n)^(2) for n = 10 and n= 11 .