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Find the sum of 1/(1!(n-1)!)+1/(3!(n-3)!...

Find the sum of `1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+ ...,`

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If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n) "show that ", (1)/(1!(n-1)!)+(1)/(3!(n-3)!)+(1)/(5!(n-5)!)+....=(2^(n-1))/(n!)

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find the coefficient of x^(13) in the expansion of (1-x)^5xx(1+x+x^2+x...

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  2. Find the sum .^(10)C1+^(10)C3+^(10)C5+^(10)C7+^(10)C9

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  3. Find the sum of 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+ ...,

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  4. If n is an even positive integer, then find the value of x if the gr...

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  5. If |x|<1, then find the coefficient of x^n in the expansion of (1+2x+3...

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  6. If (r+1)t h term is the first negative term in the expansion of (1+x)^...

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  7. If |x|<1, then find the coefficient of x^n in the expansion of (1+x+x^...

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  8. If |x|>1, then expand (1+x)^(-2)dot

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  9. Find the cube root of 27

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  10. Find the coefficient of x^2 in (a/(a+x))^(1//2)+(a/(a-x))^(1//2)

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  11. Prove that :^(10)C1(x-1)^2-^(10)C2(x-2)^2+^(10)C3(x-3)^2 .....-^(10)C(...

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  12. If the third term in the expansion of (1+x)^mi s-1/8x^2, then find the...

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  13. Prove that sum(r=0)^n r(n-r)(.^nC r)^2=n^2(.^(2n-2)Cn)dot

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  14. Prove that 1-^n C1(1+x)/(1+n x)+^n C2(1+2x)/((1+n x)^2)-^n C3(1+3x)/((...

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  15. Find the coefficient of x^(20) in (x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot

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  16. The number of terms in the expansion of (a+b+c)^n where ninN is

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  17. Find the coefficient of x^(50) in the expansion of (1+x)^(101)xx(1-x+x...

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  18. Find the coefficient of x^4 in the expansion of (2-x+3x^2)^6dot

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  19. Find the coefficient of x^k in1+(1+x)+(1+x)^2++(1+x)^n(0lt=klt=n)dot

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  20. The term independent of x in the expansion of (1+x+2x^3)(3/2(x^2)-1/(3...

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