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Find the sum sum(r=1)^n r^n (^nCr)/(^nC(...

Find the sum `sum_(r=1)^n r^n (^nC_r)/(^nC_(r-1))` .

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the sum sum(j=0)^n( ^(4n+1)Cj+^(4n+1)C(2n-j)) .

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  2. Show that no three consecutive binomial coefficients can be in G.P.

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  3. Find the sum sum(r=1)^n r^n (^nCr)/(^nC(r-1)) .

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  4. Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integ...

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  5. If the 3rd, 4th , 5th and 6th term in the expansion of (x+alpha)^n ...

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  6. Find the remainder when 7^(98) is divided by 5.

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  7. Show that 2^(4n+4)-15n-16, where n in N is divisible by 225.

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  8. If (2+sqrt(3))^n=I+f, where I and n are positive integers and 0lt f lt...

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  9. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

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  10. If 9^7+7^9 is divisible b 2^n , then find the greatest value of n ,w...

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  11. Prove that sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)] is an even ...

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  12. Find the remainder when x=5^(5^(5^(5...))) (24 times 5) is divided by ...

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  13. Find the remainder when 1690^(2608)+2608^(1690) is divided by 7.

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  14. Find the value of {3^(2003)//28}, w h e r e{dot} denotes the fractiona...

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  15. Find the remainder when 5^(99) is divided by 13.

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  16. Find the remainder when 7^(103) is divided by 25.

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  17. Using binomial theorem, prove that 6^n-5n always leaves remainder 1...

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

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

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  20. In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binom...

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