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The value of .^(n)C(1)+.^(n+1)C(2)+.^(n+...

The value of `.^(n)C_(1)+.^(n+1)C_(2)+.^(n+2)C_(3)+"….."+.^(n+m-1)C_(m)` is equal to

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Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

Find the sum .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "……" + n xx .^(n)C_(n) .

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If .^(n)C_(3)=k.n(n-1)(n-2) then k=

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If .^(n)C_(1),^(n)C_(2)and^(n)C_(3) are in A.P ., find n .

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If (1+x)^n=C0+C1x+C2x^2+...+Cn x^n , t h e n C0-(C0+C1)+(C0+C1+C2)-(C0...

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  2. In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N,

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  3. The value of .^(n)C(1)+.^(n+1)C(2)+.^(n+2)C(3)+"….."+.^(n+m-1)C(m) is ...

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  4. If (1+x)^n=C0+C1x+C2 x^2+...+Cn x^n , n in N ,then C0-C1+C2-.....+(-1...

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  5. The 10th term of (3-sqrt((17)/4+3sqrt(2)))^(20) is (a) a irrational nu...

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  6. Find the geometric mean between2a and 8a^3

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  7. Let (1+x^(2))^(2) (1+x)^(n) = underset(k = 0)overset(n+4)suma(k)x^(k)....

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  8. The middle term in the expansion of (x/2+2)^8 is 1120, then x in R is...

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  9. The sum of three numbers of GP is 39/10 and their product is 1. Find...

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

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

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

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

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  14. 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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  15. 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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  16. Find dy/dt , if y = (1 - cost)/(1 + cost) is

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

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

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

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