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prove that the coefficient of the (r +1)...

prove that the coefficient of the (r +1)th term in the expansion of `(1+x)^(n) ` is equal to the sum of the coefficients of the rth and (r+1)th terms in the expansion of `(1+x)^(n-1)`

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CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE ( short answer Type Questions )
  1. In the expansion of (1+x)^(20) , the coefficient of the rth term is to...

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  2. If in the expansion of (1+x)^(43) ,the coefficient of (3r+1)th term be...

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  3. prove that the coefficient of the (r +1)th term in the expansion of (...

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

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  5. Show that the coefficient of the middle term of (1+x)^(2m) is equal to...

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

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  7. If the coefficients of (p +1) th and (p+3)th terms in the expansion of...

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  8. Let n ge 5 b ne0, if in the binomial of (a-b)^(n), the sum of the 5th...

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  9. If the coefficients of x^(2) and x^(11) in the expansion of (1+ax+2x^(...

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  10. If in the expansion of (1+x)^(m)(1-x)^(n) the coefficients of xandx^(...

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  11. Use binomial theorem to show that if nge1 is an integer then , (a) ...

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  12. n(gt1) is a positive integer . Show that 14^(n)-13n-1 is divisible by...

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  13. For every natural number n(gt1) , show that , 4^(n)+15n-1 is divisible...

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  14. If n is a positive integer (gt1) , show that, (4^(2n+2)-15n-16) is a...

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  15. Using binomial theorem find the value : (0.999)^(4) [correct to thr...

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  16. Using binomial theorem find the value : (1.02)^(4) [correct to two ...

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  17. Write down the expansion of (4x-(y)/(4))^(4). By giving suitable valu...

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  18. Prove that , (x^(n))/(n!)+(x^(n-1).a)/((n-1)!1!)+(x^(n-2).a^(2))/((n-2...

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  19. Two successive terms in the expansion of (2+(1)/(2))^9 are equal . ...

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  20. If n be a positive integer and the sums of the odd terms ans even term...

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