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If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx...

If `(1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n` prove the following :
`C_0-C_1/2+C_2/3-.....+(-1)^n C_n/(n+1)= 1/(n+1)`.

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MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0-...

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

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

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

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

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

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  7. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0C...

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  8. Prove that C0Cr+C1 C(r+1)+ C2 C(r+2)+...............+c(n-r) Cn=((2n)!...

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  9. Find the coefficient of x^(n-r) in the expansion of (x+1)^n (1+x)^n. ...

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  10. Find the coefficient of x^4 in the expansion of (1+x)^n (1-x)^n. Deduc...

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  11. Write and simplify the term involving a^2b^5 in (a-2b)^4 (a+b)^3.

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  12. Expand using binomial theorem (1+x/2-2/x)^(4), x ne 0

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  13. Find an approximation of (0.99)^5 using the first three terms of its e...

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  14. If 6th, 7th, 8th and 9th terms of (x+y)^n are a, b,c and d respectivel...

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  15. Find the coefficient of x^10 in the expansion of : (1+x+x^2+x^3 +........

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  16. If kr is the coefficient of y^(r-1) in the expansion of (1+2y)^10, in ...

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  17. If x^p occurs in the expansion of (x^2+1/x)^(2n), prove that its coeff...

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  18. Determine the term independent of x in the expansion of (1+x+x^(-2)+x^...

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  19. Find the value of (a^2+ sqrt(a^2-1))^4+(a^2- sqrt(a^2-1))^4.

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  20. If fourth term in the expansion of : {sqrt(x^(1/(logx+1)))+x^(1/12)}^6...

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