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If (3 + 7x - 9x^2)^n = a0 +a1x + a2 x^2 ...

If `(3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n)` prove the `a_0 +a_1 +a_2 + ……+a_(2n) = 1`

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AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. Show that the middle term in the expansion of (1+x)^(2n)" is "(1.3.5. ...

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  2. Find the numerically greatest terms in the expansion of (3 + 2a)^15 ...

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  3. If (3 + 7x - 9x^2)^n = a0 +a1x + a2 x^2 + ……+a(2n)x^(2n) prove the a0 ...

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  4. If (3 + 7x - 9x^2)^n = a0 +a1x + a2 x^2 + ……+a(2n)x^(2n) prove the a0 ...

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  5. If (1+3x-2x^(2))^(10)=a(0)+a(1)x+a(2)x^(2).+…+a(20)x^(20) then prove t...

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  6. If (1+3x-2x^(2))^(10)=a(0)+a(1)x+a(2)x^(2).+…+a(20)x^(20) then prove t...

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  7. If (1 + 3x - 2x^2)^10 = a0 + a1x + a2x^2 +…..+a20 x^20 thn prove that ...

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  8. If (1 + 3x - 2x^2)^10 = a0 + a1x + a2x^2 +…..+a20 x^20 thn prove that ...

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  9. If the 2^("nd"),3^("rd")" and "4^("th") terms in the expansion of (a+x...

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  10. If the coefficients of x^(9),x^(10),x^(11) in expansion of (1+x)^(n) a...

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  11. If n is a positive integer, then prove that 81^n + 20 n - 1 is divisib...

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  12. Using binomial theorem, prove that 5^(4n)+52n-1 is divisible by 676 fo...

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  13. 3. C0 + 7. C1 + 11. C2 +…...+ (4n+3) . Cn=

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  14. With usual notations find the value of 3.C1 + 5.C2 + 7.C3 + ……….+n ter...

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  15. With usual notations prove that C1+2.C2x + 3.C3x^2 + ……+2n.C(2n) ...

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  16. Prove that (""^20C1)/(""^20C0) + 2. (""^20C2)/(""^20C1) + 3. (""^2...

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  17. If n is a positive integer and C4 = ""^nCr then find the value of sum(...

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  18. Prove that sum(r = 1)^(n+1) (2^(r +1) C(r - 1) )/(r (r + 1)) = (3^(n+...

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  19. Prove that sum(r = 0)^n r^2 . Cr = n (n +1).2^(n-2)

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  20. Prove that sum(r = 0)^n r^3 . Cr = n^2 (n +3).2^(n-3)

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