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If `a_1,a_2, a_3, a_4` be the coefficient of four consecutive terms in the expansion of `(1+x)^n ,` then prove that: `(a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)dot`

A

`(a_(2))/(a_(2)+a_(3))`

B

`(1)/(2) (a_(2))/(a_(2)+a_(3))`

C

`(2a_(2))/(a_(2)+a_(3))`

D

`(2a_(3))/(a_(2)+a_(3))`

Text Solution

Verified by Experts

The correct Answer is:
c
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ML KHANNA-BINOMIAL THEOREM AND MATHEMATICAL INDUCTION -Problem Set (2) (MULTIPLE CHOICE QUESTIONS)
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  2. If C(0),C(1),C(2),… C(15) are the binomial coefficients in the expans...

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  3. If C(r )=""^(n)C(r ), then the value of 2((C(1))/(C(0)) +2(C(2))/(...

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  4. In the expansion of (1+x)^(n) the binomial coefficients of three con...

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  5. If the secound, third and fourth terms in the expansion of (x + y )...

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  6. If the 21st and 22nd terms in the expansion of (1 - x)^(44) are equal...

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  7. If the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the expan...

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  8. If in the expansion of (1+x)^n the coefficients of 14th, 15th and 16th...

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

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  10. If the coefficients of three consecutive terms in the expansion of (1+...

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  11. If the coefficients of second, third and fourth terms in the expansion...

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  12. Let n be positive integer. If the coefficients of 2nd, 3rd and 4th te...

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  13. If the coefficient of the middle term in the expansion of (1+x)^(2n+2)...

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  14. If a1,a2, a3, a4 be the coefficient of four consecutive terms in the e...

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  15. The greatest coefficient in the expansion of (1 + x)^(10), is

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  16. The greatest coefficient in the expansion of (1+x)^(2n+2) is

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  17. Two consecutive terms in the expansion of (3+2x)^74 have equal coeffic...

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  18. Find the largest term in the expansion of (3+2x)^(50),w h e r ex=1//5.

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

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  20. In the binomial expansion (a-b)^n, nge5 the sum of 5th and 6th terms i...

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