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If a(1), a(2), a(3), a(4) are the coeff...

If `a_(1), a_(2), a_(3), a_(4)` are the coefficients of the `2^(nd), 3^(rd), 4^(th) and 5^(th)` terms respectively in the binomial expansion of `(1+x)^(n)` where n is a positive integer prove that `(a_(1))/(a_(1)+a_(2)) , (a_(2))/(a_(2)+a_(3)) , (a_(3))/(a_(3)+a_(4))` are in arithmetic progression.

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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - 1.1 (Level - 1)
  1. If (1+x+x^(2))^(n)=b(0)+b(1)x+b(2)x^(2)+….+b(2n)x^(2n) then prove that...

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  2. Prove that AA n in N 3^(3n)-26n-1 is divisible by 676.

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  3. Prove that AA n in N 6^(n)-5n leaves remainder 1 when divided by 25...

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  4. Prove that AA n in N 9^(n+1)-8n-9 is divisible by 64

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  5. Prove that AA n in N 5^(4n)+52n-1 is divisible by 676.

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  6. If the coefficient of x^7 in (ax^2+(1)/(bx))^11 equals the coefficient...

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  7. Show that the number of terms with integral values in the expansion of...

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  8. Find the coefficient of x^(7) in the expansion of (1-x-x^(2)+x^(3))^(6...

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  9. Find the coefficient of x^(3) in the expansion of (2-x+5x^(2))^(6).

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  10. If the coefficients of r^("th"),(r+1)^("th") and (r+2)^("nd") terms in...

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  11. If a(1), a(2), a(3), a(4) are the coefficients of the 2^(nd), 3^(rd),...

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  12. If P and Q are the sum of odd terms and the sum of even terms respecti...

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  13. If P and Q are the sum of odd terms and the sum of even terms respecti...

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  14. Simplify the following (sqrt(3)+sqrt(2))^(4)-(sqrt(3)-sqrt(2))^(4)

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  15. Simplify the following (sqrt(2)+1)^(5) +(sqrt(2)-1)^(5)

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  16. Simplify the following (sqrt(3)+1)^(5) -(sqrt(3) -1)^(5)

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  17. Simplify the following (sqrt(x+1) + sqrt(x-1))^(6) +(sqrt(x+1) - sqr...

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  18. Using binomial theorem, prove that 50^(n)-49n-1 is divisible by 49^(2)...

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

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  20. Find the remainder when 2^(2013) in divided by 17.

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