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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`.

A

`n^(2)-n(4r+1)+4r^(2)-2=0`

B

`n^(2)+n(4r+1)+4r^(2)-2=0`

C

`n^(2)+n(4r+1)+4r^(2)+2=0`

D

`n^(2)+n(4r+1)+4r^(2)+2=0`

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NAGEEN PRAKASHAN ENGLISH-BINOMIAL THEOREM-Exercise 8F
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  3. If the second, third and fourth terms in the expansion of (x+y)^(n) be...

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  4. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

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  5. If a. b, c and d are the coefficients of 2nd, 3rd, 4th and 5th terms r...

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  6. If the coefficients of x^7 and x^8 in the expansion of [2 +x/3]^n a...

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  7. If A and B denote the coefficients of x^(n) in the binomial expansi...

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  8. Find the greatest term in the expansion of sqrt(3)(1+1/(sqrt(3)))^(20)...

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

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  10. if the coefficients of x^(5)" and "x^(15) in the expansion of (x^(2)+(...

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  11. Find the coefficient of x^4 in the expansion of (2-x+3x^2)^6dot

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  12. If the sum of the coefficients in the expansion of (a+b)^n is 4096, th...

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  13. If the second, third and fourth terms in the expansion of (x+y)^(n) be...

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  14. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

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  15. if a,b,c and d are the coefficient of four consecutive terms in the ex...

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  16. If the coefficients of x^(7) and x^(8) in the expansion of (2+x/3)^(n)...

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  17. If A and B are the coefficients of x^n in the expansion (1 + x)^(2n) a...

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  18. Find the greatest term in the expansion of sqrt(3)(1+1/(sqrt(3)))^(20)...

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  19. If the coefficients of the rth, (r+1)t h ,(r+2)t h terms is the expans...

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  20. if the coefficients of x^(5)" and "x^(15) in the expansion of (x^(2)+(...

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