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Show that 9^(n+1)-8n-9 is divisible by 6...

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

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By principle of mathematical induction show that a^(n)-b^(n) is divisible by a+b when n is a positive even integer.

By using mathematical induction prove that 3^(2n)-8n-1 is divisible by 64 when n is an integer.

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Show that no three consecutive binomial coefficients can be in G.P.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Using binomial theorem prove that 6^n-5n always leaves remainder I whe...

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

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

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

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  20. Prove that (C0+C1)(C1+C2)(C2+C3)(C3+C4)...........(C(n-1)+Cn) = (C0...

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