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If t0,t1, t2,...,tn are the terms in the...

If `t_0,t_1, t_2,...,t_n` are the terms in the expansion of `(x+a)^n` then prove that `(t_0-t_2+t_4-...)^2+(t_1-t_3+t_5-...)^2=(x^2+a^2)^n`.

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. Find the sum :1/2*""^(n)C0+""^(n)C1+2*""^(n)C2+2^2*""^nC3+...+2^(n-1)*...

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  2. Prove that : (1+""^nC1+""^nC2+""^nC3+...+""^nCn)^2=1+""^(2n)C1+""^(2n)...

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  3. If t0,t1, t2,...,tn are the terms in the expansion of (x+a)^n then pro...

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  4. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a1+a2+….

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  5. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0-a1+a2......

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  6. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a2+a4+…

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  7. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a1+a3+a5+…

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  8. 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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  9. 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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  10. 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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  11. 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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  12. The sum of the binomial coefficients in the expansion of (x^2+1/x)^n i...

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  13. The exponent of a binomial exceeds that of another by 3. the sum of th...

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  14. Find the coefficient of x^3 in the expansion of 1+(1+x)+(1+x)^2+(1+x)^...

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  15. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

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  16. (b) Find the value of sum(r=m)^n .^rCm,n>m

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  17. Evaluate (""^3C3+""^4C3+""^5C3+...+""^nC3)xx(""^nC3+""^nC4+""^nC5+...+...

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  18. 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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  19. Prove that ""^(n+1)C2+2*sum(k=2)^n""^kC2=sum(k=1)^nk^2

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  20. If (1+x)^n=C0+C1x+C2x^2+...+Cnx^n , find the sum of the following seri...

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