Home
Class 12
MATHS
If ( 1 + x - 2x^(2))^(20) = sum(r=0)^(4...

If ` ( 1 + x - 2x^(2))^(20) = sum_(r=0)^(40) a_(r) x^(r) ` , then find
the value of ` a_(1) + a_(3) + a_(5) + …+ a_(39)` .

A

`2^(19) (2^(19- 20)`

B

`2^(19) (2^(20) - 21)`

C

`2^(19) (2^(19) - 21)`

D

`2^(19) (2^(19) -19)`

Text Solution

Verified by Experts

The correct Answer is:
b
` a_(1) + a_(2) + a_(4) + …+ a_(38) + a_(40) = 2^(19) (2^(20) + 1) " " ` [from Eq. (iii) ]
` rArr a_(0) + a_(2) + a_(4) + …+ a_(38) = 2^(19) (2^(20) +1) - a_(40) `
` = 2^(19) (2^(20) + 1) - 2^(20) " " ` [ From Eq . (vi)]
` = 2^(19) (2^(20) -1) `
Promotional Banner

Similar Questions

Explore conceptually related problems

(1+x-2x^(2))^(6)=1+a_(1),x+a_(2)x^(2)+….+a_(12)^(12) then the value of a_(2) +a_(4)+a_(6)+….+a_(12)=………

What does a_(1) + a_(2) + a_(3) + …..+ a_(n) represent

If a_(i) gt 0 AA I in N such that prod_(i=1)^(n) a_(i) = 1 , then prove that (a + a_(1)) (1 + a_(2)) (1 + a_(3)) .... (1 + a_(n)) ge 2^(n)

Find the relation between acceleration of blocks a_(1), a_(2) and a_(3) .

If a_(1),a_(2),a_(3),a_(4) and a_(5) are in AP with common difference ne 0, find the value of sum_(i=1)^(5)a_(i) " when " a_(3)=2 .

If a_(1),a_(2),a_(3),"........" is an arithmetic progression with common difference 1 and a_(1)+a_(2)+a_(3)+"..."+a_(98)=137 , then find the value of a_(2)+a_(4)+a_(6)+"..."+a_(98) .

p(x)=a_(0)+a_(1)x^(2)+a_(2)x^(4)+…………+a_(n)x^(2n) is a polynomial with real variable x. If 0 lt a_(0)lt a_(1)lt a_(2)lt ……….lt a_(n) then p(x) has …………

if (1+ax+bx^(2))^(4)=a_(0) +a_(1)x+a_(2)x^(2)+…..+a_(8)x^(8), where a,b,a_(0) ,a_(1)…….,a_(8) in R such that a_(0)+a_(1) +a_(2) ne 0 and |{:(a_(0),,a_(1),,a_(2)),(a_(1),,a_(2),,a_(0)),(a_(2),,a_(0),,a_(1)):}|=0 then the value of 5.(a)/(b) " is " "____"

Find the sum of first 24 terms of the A.P. a_(1) , a_(2), a_(3) ...., if it is know that a_(1) + a_(5) + a_(10) + a_(15) + a_(20) + a_(24) = 225