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)`
For all values of a show that
`(C_(0))/(a)-(C_(1))/(a+a)+(C_(2))/(a+2)-...+(-1)^(n)(C_(n))/(a+n)=(n!)/(a(a+1)(a+2)...(a+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) then show : (C_(0))/(1)-(C_(1))/(2)+(C_(2))/(3)-......+(-1)^(n).(C_(n))/(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))/(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_(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_(1))/(2)+(C_(3))/(4)+(C_(5))/(6)+....=(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_(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_(1))/(C_(0))+(2C_(2))/(C_(1))+(3C_(3))/(C_(2))+....+(nC_(n))/(C_(n-1))=(n(n-1))/(2)

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n)

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that C_(0) *""^(2n)C_(n) - C_(1) *""^(2n-2)C_(n) + C_(2) *""^(2n-4) C_(n) -…= 2^(n)

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(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
|
If S(1), S(2), S(3),...S(n) are the sums of infinite geometric series,...
Text Solution
|
If u(r)=(1)/(r!) then show that u(0)u(n)+8u(1)+u(n-1)+8^(2)u(2)u(n-2...
Text Solution
|