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If underset(r=0)overset(n)sum((r+2)/(r+1...

If `underset(r=0)overset(n)sum((r+2)/(r+1)).^(n)C_(r)=(2^(8)-1)/(6)`. then nis

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If sum_(r=0)^(n)((r+2)/(r+1)).^n C_r=(2^8-1)/6 , then n is (A) 8 (B) 4 (C) 6 (D) 5

If (1+x^(2))^(n) = underset(r=0)overset(n)suma_(r)x^(r )= (1+x+x^(2)+x^(3))^(100) . If a = underset(r=0)overset(300)suma_(r) , then underset(r=0)overset(300)sumra_(r) is

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Prove that underset(r=1)overset(n)sum "tan"^(-1)(2r)/(r^(4)+r^(2)+2)="tan"^(-1)(n^(2)+n+1)-(pi)/(4)

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. The sum of three numbers of GP is 39/10 and their product is 1. Find...

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  2. The first two term of a G.P are 125, and 25 respectively. Find the 5t...

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  3. If underset(r=0)overset(n)sum((r+2)/(r+1)).^(n)C(r)=(2^(8)-1)/(6). the...

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  4. Let f(x) = a(0) + a(1)x + a(2)x^(2) + "…." + a(n)x^(n) + "…." abd (f(x...

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  5. If (1+x^(2))^(n) = underset(r=0)overset(n)suma(r)x^(r )= (1+x+x^(2)+x^...

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  6. The value of sum(r=1)^(n+1)(sum(k=1)^n^kC(r-1)) (where r, k, n in N) i...

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  7. If (x^(2)+x+1)/(1-x) = a(0) + a(1)x+a(2)x^(2)+"….", then sum(r=1)^(50...

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  8. Find dy/dt , if y = (1 - cost)/(1 + cost) is

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  9. The coefficient of x^9 in the expansion of (1+x)(1+x^2)(1+x^3)....(1+x...

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  10. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

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  11. If (1-x)^(-n)=a0+a1x+a2x^2++ar x^r+ ,t h e na0+a1+a2++ar is equal to ...

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  12. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to ?

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  13. The coefficient of x^(10) in the expansion of (1+x^(2)-x^(3))^(8) is

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  14. If the term independent of x in the (sqrt(x)-k/(x^2))^(10) is 405, the...

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  15. The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (a)(20 !...

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  16. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is

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  17. The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d +b c d)^(10) is

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  18. If the coefficient of x^(7)in [ax^(2) + (1/bx)]^(11) equals the coeffi...

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  19. If (1+x)^5=a0+a1x+a2x^2+a3x^3+a4x^4+a5x^5, then the value of (a0-a2+a4...

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  20. The coefficient of x^n in the expansion of (1+x)(1-x)^n is

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