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)`
Show that `C_(0)^(2)+2C_(1)^(2)+3C_(2)^(2)+...+(n+1)*C_(n)^(2)=((n+2)(2n-1)!)/(n!(n-1)!)`

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 show : C_(0)^(2)+(C_(1)^(2))/(2)+(C_(2)^(2))/(3)+.....+(C_(n)^(2))/(n+1)=((2n+1)!)/({(n+1)!}^(2))

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

Prove that, C_(0)^(2)+C_(1)^(2)+C_(2)^(2)+.......+C_(n)^(2)=((2n)!)/(n!)^(2)

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

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) , show that, (C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+…+(C_(n))/(n+1)=(2^(n+1))/(n+1)

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

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA

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
|
For every natural number n, show that 7^(2n)+2^(3n-3)*3^(n-1) is alway...
Text Solution
|
If the coefficients of the (r-1) th and (2r+3) th terms in the equatio...
Text Solution
|
If n is a positive integer then using the indentiy (1+x)^(n)=(1+x)^(3)...
Text Solution
|