If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C...

If `(1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n)`
Find the value of `C_(1)+2^(2)C_(2)x+3^(2)C_(3)x^(2)+...+n^(2)C_(n)x^(n-1)` and hence find the sum of `C_(1)-2^(2)C_(2)+3^(2)C_(3)-.... +(-1)^(n-1)n^(2)*C_(n)`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

MISCELLANEOUS EXAMPLES
CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)|124 Videos
MISCELLANEOUS EXAMPLES
CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos
MISCELLANEOUS EXAMPLES
CHHAYA PUBLICATION|Exercise TRIGONOMETRY|148 Videos
METHOD OF SUBSTITUTION
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos
ORDER AND DEGREE OF DIFFERENTIAL EQUATION
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n) Show that C_(1)^(2)+2*C_(2)^(2)+3*C_(3)^(2)....+n*C_(n)^(2)=((2n-1)!)/([(n-1)!]^(2))

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n)x^(n) show that, C_(0)-2^(2)*C_(1)+3^(2)*C_(2)-...+(-1)^(n)*(n+1)^(2)*C_(n)=0 (n gt 2)

If (1+x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + "….." + C_(n)x^(n) , then find the value of C_(0)+C_(2)+C_(4)+C_(6)+........

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(1)+2.C_(2)+3.C_(3)+....+n.C_(n)=n.2^(n-1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(1)-2C_(2)+3C_(3)-....+(-1)^(n-1)n.C_(n)=0

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(1))/(2)+(C_(3))/(4)+(C_(5))/(6)+....=(2^(n)-1)/(n+1)

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

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)+(C_(2))/(3)+(C_(4))/(5)+....=(2^(n))/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+......+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(0)+4C_(1)+8C_(2)+12C_(3)+......+4nC_(n)=1+n.2^(n+1)

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA

Using mathematical induction prove that, tan^(-1)((1)/(2*1^(2)))+tan...
Text Solution
|
If (1+x+x^(2))^(n)=a(0)+a(1)+x+a(2)x^(2)+...+a(2n)x^(2n), show that a(...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Find the value of ...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that C(1)-(1)...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that 1^(2)*C...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that C(0)^(2)...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that (2^(2)*C...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) For all values of ...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that C(1)^(2)...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) show that (C(0))^(...
Text Solution
|
Show that the sum of the coefficient of first (r+1) terms in the expan...
Text Solution
|
Show that 4^(m)[ 1+(m)/(2)+(m(m+1))/(2*4)+(m(m+1)(m+2))/(2*4*6)+...] ...
Text Solution
|
It is given that n is an odd integer greater than 3 but n is not multi...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n)x^(n) show that, 1^(2)*C...
Text Solution
|
If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n)x^(n) show that, C(0)-2^(...
Text Solution
|
Using binomial theorem for a positive integral index, prove that (2^(3...
Text Solution
|
Find the largest coefficient in the expansion of (1+x)^(n), given that...
Text Solution
|
Given that the 4th term in the expansion of (2+(3)/(8)x)^(10) has the ...
Text Solution
|
If x in RR then find the solution set of the inquation |3x-7| gt 4.
Text Solution
|
Solve the following quadratic equation: \ x^2-(5-i)x+(18+i)=0
Text Solution
|