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If the coefficient of the rth, `(r+1)th and (r+2)th` terms in the expansion of `(1+x)^(n)` are in A.P., prove that `n^(2) - n(4r +1) + 4r^(2) - 2=0`.

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ICSE-BINOMIAL THEOREM-EXERCISE 13 (b)
  1. Write down the fourth term in the binomial expansion of (px + (1)/(x) ...

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  2. The expansion by the binomial theorem of (2 x + (1)/(8) )^(10) is 1024...

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  3. The expansion by the binomial theorem of (2 x + (1)/(8) )^(10) is 1024...

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  4. The expansion by the binomial theorem of (2 x + (1)/(8) )^(10) is 1024...

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  5. Find the coefficient of x^7 in ( ax^(2) + (1)/( bx) )^(11) and the coe...

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  6. In a binomial expansion, ( x+ a)^(n), the first three terms are 1, 56 ...

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  7. Write the 4th term from the end in the expansion of ((x^3)/( 2) - (2)/...

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  8. The coefficients of (2r +1)th and (r+2)th terms in the expansions of (...

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  9. The coefficient of the middle term in the binomial expansion in powers...

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  10. Find the sixth term of the expansion of (y^(1//2) + x^(1//3) )^(n), if...

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  11. Show that the coefficient of the middle term in the expansion of (1 + ...

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  12. Show that the middle term in the expansion of (1+ x)^(2n) is (1.3.5…(...

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  13. Find the coefficient of x^5 in the expansion of 1+(1+x)+ (1+x)^2 + … +...

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

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  15. If P be the sum of odd terms and Q be the sum of even terms in the exp...

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  16. If P be the sum of odd terms and Q be the sum of even terms in the exp...

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  17. If P be the sum of odd terms and Q be the sum of even terms in the exp...

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  18. If the coefficient of the rth, (r+1)th and (r+2)th terms in the expans...

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  19. In the expansion of (x^(2) + (1)/(x) )^(n), the coefficient of the fou...

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  20. The coefficient of x^(n) in the expansion of (1+x)(1-x)^(n) is

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