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The coefficients of three consecutive te...

The coefficients of three consecutive terms in the expansion of `(1+a)^(n)` are in the ratio `1 : 7 : 42`. Find n

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MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. Find a, b and n in the expansion of (a + b)^(n) if the first three ter...

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  2. The first three terms in the expansion of a binomial are 1, 10 and 40....

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  3. The coefficients of three consecutive terms in the expansion of (1+a)^...

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  4. The coefficients of three consecutive terms in the expansion of (1+a)^...

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  5. If the coefficients of 5th, 6th , and 7th terms in the expansion of (1...

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  6. If the coefficients of x, x^2 and x^3 in the binomial expansion of (1+...

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  7. If three successive coefficients in the expansion of (1+x)^n are 28, 5...

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  8. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

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  9. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

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  10. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

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  11. Show that 9^(n+1) - 8n -9 is divisible by 64, whenever n is a positiv...

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  12. Using Binomial theorem, prove that 6^(n)-5n always leaves remainder 1...

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  13. Evaluate the following : ""^12C0+""^12C1+""^12C2+ ....... +""^12C12.

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  14. Evaluate the following : ""^12C0+""^12C2+""^12C4 +""^12C12.

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  15. Evaluate the following : ""^16C1+""^16C3+""^16C5+ ....... +""^16C15.

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  16. Prove that underset (r=0) overset (n) sum 3^r ""^nCr =4^n.

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  17. Prove that ""^nC0+3""^nC1+5""^nC2+........+(2n+1)""^nCn= (n+1)2^n.

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  18. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0-...

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  19. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : (1+...

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  20. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0-...

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