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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
- The sum of the series 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+…..+1/((n...
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- Find the sum :1/2*""^(n)C0+""^(n)C1+2*""^(n)C2+2^2*""^nC3+...+2^(n-1)*...
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- Prove that : (1+""^nC1+""^nC2+""^nC3+...+""^nCn)^2=1+""^(2n)C1+""^(2n)...
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- If t0,t1, t2,...,tn are the terms in the expansion of (x+a)^n then pro...
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- If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a1+a2+….
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- If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0-a1+a2......
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- If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a2+a4+…
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- If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a1+a3+a5+…
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- If (1+x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a0+a1+a2...
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- If (1+x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a0-a1+a2...
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- If (1+2x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a0+a2+a...
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- If (1+x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a1+a3+a5...
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- 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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