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If n is a positive integer, show that, i...

If n is a positive integer, show that, in the expansion of `(1+x)^(n)` the sum of the coefficents of terms in the odd positions is equal to the sum of the cofficients of term in the even positions and each sum is equal to `2^(n-1)`.

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CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE (Very short answer Type Questions )
  1. State the binomial theorem for a positive integral index.

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  2. If n is a positive integer, show that, in the expansion of (1+x)^(n) t...

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  3. Write down the binominal expansion of , (a+2b)^(5)

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  4. Write down the binominal expansion of , (a-3/b)^(7)

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  5. Write down the binominal expansion of , (x/3 + 2/t)^(4)

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  6. Write down the dimension of entropy.

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  7. Write down the binominal expansion of , (x^(3)-3x^(2)y + 3xy^(2)-y...

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  8. Write down the binominal expansion of , (x^(2)-x-2)^(3)

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  9. Write down the binominal expansion of , (1-x+x^(2))^(4).

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  10. Simplify : (sqrt(3)+1)^(5)-(sqrt(3)-1)^(5)

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  11. Simplify : (2+sqrt(3))^(6) + (2-sqrt(3))^(6)

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  12. Simplify : (x+y)^(4) - 4y(x+y)^(3) + 6y^(2)(x+y)^(2)-4y^(3)(x+y)+y^(...

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  13. Simplify : (a-3)^(3) + 6(a-3)^(2)+12(a-3)+8

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  14. Simplify : (x+sqrt(x^(2)-1))^(7) + (x-sqrt(x^(2)-1))^(7)

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  15. Expand (3x-5/(x^3))^(8) up to the term independent of x.

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  16. Determine: 10th term in the expansion of (3a+2/a)^(12)

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  17. Determine: 4th term in the expansion of (a/b-b/a)^(10)

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  18. Determine: nth term in the expansion of (x+1/x)^(2n)

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  19. Determine: the general term in the expansion of (a-1/(3a))^(m)

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  20. 5th term from the end in the expansion of ((x^3/2)-(2/x^2))^12 is

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