In the coefficients of rth, (r+1)t h ,a ...

In the coefficients of rth, `(r+1)t h ,a n d(r+2)t h` terms in the binomial expansion of `(1+y)^m` are in A.P., then prove that `m^2-m(4r+1)+4r^2-2=0.`

A

`m^(2)-m(4r-1)+4r^(2)+2=0`

B

`m^(2)-m(4r+1)+4r^(2)-2=0`

C

`m^(2)-m(4r+1)+4r^(2)+2=0`

D

`m^(2)-m(4r-1)+4r^(2)-2=0`

Text Solution

Verified by Experts

The correct Answer is:

B

Topper's Solved these Questions

BINOMIAL THEOREM
VMC MODULES ENGLISH|Exercise LEVEL 2|50 Videos
BINOMIAL THEOREM
VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|14 Videos
BINOMIAL THEOREM
VMC MODULES ENGLISH|Exercise JEE Archive|56 Videos
CIRCLES
VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

Similar Questions

Explore conceptually related problems

If the coefficient of the rth, (r+1)th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P., prove that n^(2) - n(4r +1) + 4r^(2) - 2=0 .

If the coefficient of r^(th) ,( r +1)^(th) " and " (r +2)^(th) terms in the expansion of (1+x)^n are in A.P then show that n^2 - (4r +1)n + 4r^2 - 2 =0

If the coefficients of r^(th) , (r + 1)^(th) and (r + 2)^(th) terms in the binomial expansion of (1 + y)^m are in A.P. then find the equation m and r satisfy

If the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the expansion of (1+x)^(14) are in A.P., then r is/are a. 5 b. 11 c. 10 d. 9

If the coefficients of the rth, (r+1)t h ,(r+2)t h terms is the expansion of (1+x)^(14) are in A.P, then the largest value of r is.

If the coefficients of (r-5)t h a n d(2r-1)t h terms in the expansion of (1+x)^(34) are equal, find rdot

If the coefficients of a^(r-1),\ a^r and \ a^(r+1) in the binomial expansion of (1+a)^n are in A.P., prove that n^2-n(4r+1)+4r^2-2=0.

If the coefficients of rth, (r + 1)th and (r + 2)th terms in the expansion of (1 + x)^n be in H.P. then prove that n is a root of the equation x^2 - (4r - 1) x + 4r^2 = 0.

If the coefficients of (r-5)^(t h) and (2r-1)^(t h) terms in the expansion of (1+x)^(34) are equal, find r .

VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 1

Statement - 1 sum(r=0)^(n) (r + 1) ""^(n)C(r) = (n+2)*2^(n-1) Stat...
Text Solution
|
if n>=2, ""^(n+1)C(2)+2(""^(2)C(2)+""^(3)C(2)+""^(4)C(2)+....+""^(n)...
Text Solution
|
In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binom...
Text Solution
|
If s(n)=sum(r=0)^(n)(1)/(.^(n)C(r))and t(n)=sum(r=0)^(n)(r)/(.^(n)C(r)...
Text Solution
|
The sum ""^(20)C(0)+""^(20)C(1)+""^(20)C(2)+……+""^(20)C(10) is equal t...
Text Solution
|
Find the coefficient of x^5 in (1+2x+3x^2...........)^(-3/2)
Text Solution
|
The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(...
Text Solution
|
The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. ...
Text Solution
|
The reamainder left out when 8^(2n) - (62)^(2n+1) is divided by 9 is
Text Solution
|
If ak is the coefficient of x^k in the expansion of (1+x+x^2)^n for k ...
Text Solution
|
The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b....
Text Solution
|
The coefficient of x^(n) in the polynomial (x+.^(n)C(0))(x+3.^(n)C(1))...
Text Solution
|
If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...
Text Solution
|
The value of sum(r=0)^nsum(s=0)^nsum(t=0)^nsum(u=0)^n(1) is
Text Solution
|
If n is an even natural number , find the value of sum(r=0)^(n) ((...
Text Solution
|
sum(r=0)^n(-2)^r*(nCr)/((r+2)Cr) is equal to
Text Solution
|
If (1+2x+3x^2)^(10)=a0+a1x+a2x^2++a(20)x^(20),t h e na1 equals 10 b. 2...
Text Solution
|
The remainder, if 1+2+2^2++2^(1999) is divided by 5 is.
Text Solution
|
The value of ((""^(50)C(0))/(1)+(""^(50)C(2))/(3)+(""^(50)C(4))/(5)+…....
Text Solution
|
In the expansion of (1+x+x^3+x^4)^10, the coefficient of x^4 is ^40C4 ...
Text Solution
|