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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
- The sum of the binomial coefficients in the expansion of (x^2+1/x)^n i...
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- The exponent of a binomial exceeds that of another by 3. the sum of th...
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- Find the coefficient of x^3 in the expansion of 1+(1+x)+(1+x)^2+(1+x)^...
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- Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...
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- (b) Find the value of sum(r=m)^n .^rCm,n>m
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- Evaluate (""^3C3+""^4C3+""^5C3+...+""^nC3)xx(""^nC3+""^nC4+""^nC5+...+...
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- The value of ^n C1+^(n+1)C2+^(n+2)C3++^(n+m-1)Cm is equal to ^m+n C(n-...
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- Prove that ""^(n+1)C2+2*sum(k=2)^n""^kC2=sum(k=1)^nk^2
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- If (1+x)^n=C0+C1x+C2x^2+...+Cnx^n , find the sum of the following seri...
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- Prove that ""^nC0+2*""^nC1+3*""^nC2+...+(n+1)""^nCn=(n+2)2^(n-1)
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- Prove that ""^nC0+3*""^nC1+5*""^nC2+...+(2n+1)""^nCn=(n+1)2^(n)
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- Prove that ""^nC0-2*""^nC1+3*""^nC2-...+(-1)""^n(n+1)""^nCn=0
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- If sn=""^nC0+2*""^nC1+3*""^nC2+...+(n+1)*""^nCn then find sum(n=1)^oos...
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- Find the sum :1*""^nC0+2*""^nC1+3*""^nC2+4*""^nC3+…, where n is an odd...
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- Show that :""^nC0*m-""^nC1*(m-1)+""^nC2*(m-2)-...+(-1)^n*""^nCn*(m-n)=...
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- Evaluate sum(r=1)^npr/r*"^nCr where pr denotes the sum of the first r ...
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- Prove by binomial expansion that sum(k=1)^nk^2*"^nCk=n(n+1)2^(n-2)
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- Evaluate sum(r=0)^n(r+1)^2*"^nCr
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- If (1+x)^n=C0+C1x+C2x^2+C3x^3+...+Cnx^n then prove that 2.C0+2^2C1/2+2...
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- If (1+x)^n=C0+C1x+C2x^2+C3x^3+...+Cnx^n then prove that C0-1/2C1+1/3C2...
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