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Find the sum C0-C2+C4-C6+ ......... ,whe...

Find the sum `C_0-C_2+C_4-C_6+ ......... `,where `C_r=^n C_r` .

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. If (1+x+x^2++x^p)^n=a0+a1x+a2x^2++a(n p)x^(n p), then find the value o...

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  2. If n >2, then prove that C1(a-1)-C2xx(a-2)++(-1)^(n-1)Cn(a-n)=a ,w h e...

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  3. Find the sum C0-C2+C4-C6+ ......... ,where Cr=^n Cr .

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  4. If x+y=1, prove that sum(r=0)^n .^nCr x^r y^(n-r) = 1.

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  5. Find the sum 3 C1 + 5C2

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  6. Prove that (.^(n)C(1))/(2) + (.^(n)C(3))/(4) + (.^(n)C(5))/(6) + "…." ...

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  7. If (1+x)^n=sum(r=0)^n^n Cr , show that C0+(C1)/2++(Cn)/(n+1)=(2^(n+1...

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  8. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

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  9. Statement 1: 3^(2n+2)-8n-9 is divisible by 64 ,AAn in Ndot Statement...

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  10. Statement 1: The number of distinct terms in (1+x+x^2+x^3+x^4)^(1000)i...

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  11. Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=s...

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  12. Statement 1:Three consecutive binomial coefficients are always in A.P....

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  13. The value of ((30), (0))((30), (10))-((30), (1))((30),( 11)) +(30 2)(3...

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  14. If f(x)=x^n ,f(1)+(f^1(1))/1+(f^2(1))/(2!)+(f^n(1))/(n !),w h e r ef^r...

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  15. The fractional part of 2^(4n)/15 is (n in N) (A) 1/15 (B) 2/15 (C) 4/1...

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  16. The value of .^(15)C(0)^(2)-.^(15)C(1)^(2)+.^(15)C(2)^(2)-"...."-.^(15...

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  17. If the sum of the coefficients in the expansion of (1-3x+10 x^2)^ni sa...

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  18. If (1+x-2x^2)^6=1+a1x+a2x^(2)++a(12)x^(12), then find the value of a2+...

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  19. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is ...

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