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If the coefficients of four consecutive terms in the expansion of `(1+x)^n` are `a_1,a_2,a_3` and `a_4` respectively. then prove that `a_1/(a_1+a_2)+a_3/(a_3+a_4)=2a_2/(a_2+a_3).

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PATHFINDER-BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
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  2. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x...

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  3. If the coefficients of four consecutive terms in the expansion of (1+x...

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  5. The coefficient of three consecutive terms in the expansion of (1+x)^n...

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  7. Show that the integral part of the value of (9+4sqrt5)^n is odd for po...

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  8. If the 3rd, 4th. 5th and sixth term in the expansion of (x+alpha)^n ar...

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  9. If coefficient of x^2 and x^11 are 27 and -192 respectively of (1+ax+2...

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  10. Find the coefficient of x^5 in the expansion of (1+x)^21+(1+x)^22+...+...

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  11. Determine the x-independent term in the expansion of (1+4x)^p(1+1/(4x)...

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  12. For ninN , 2^(3n)-1 is divisible by

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  13. For ninN , n^3+2n is divisible by

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  14. ForninN , 3^(2n-1)+2^(n+1) is always divisible by

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  15. For ninN 2^(3n)-7n-1 is always divisible by

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  16. The greatest positive integer divides (n+1)(n+2)..........(n+r) is

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  17. Applying the principle of mathematical induction (P.M.I.) prove that 1...

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  18. Using mathematical induction show 7+77+777+......+n terms =7/81(10^(n+...

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  19. Applying P.M.I. prove that x^n-y^n is always divisible by x+y where n...

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  20. Applying the principle mathematical induction (P.M.I.) show that 5^(2n...

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