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Prove that x^n-y^n is divisible by x - y...

Prove that `x^n-y^n` is divisible by x - y for all positive integers n.

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p(n) is true for all `n in N`
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FULL MARKS-COMBINATORICS AND MATHEMATICAL INDUCTION-ADDITIONAL QUESTIONS
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  5. If ""^(22)P(r+1):^(20)P(r+2)=11:52, find r.

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  6. If ""^(nP(r)=""^(n)P(r+1) and ""^(n)C(r)=""^(n)C(r-1) find n and r.

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  7. A committee of 7 peoples has to be formed from 9 men and 4 women . In ...

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  8. In .^(2n)C(3) :.^(n)C(3) = 11 : 1 then n is

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  10. If 1/(7!)+1/(9!)=x/(10!), find x.

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  11. If ""^(n)C(4),^(n)C(5)" and "^(n)C(6) are in A.P. then find n.

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  12. Prove by induction the inequality (1+x)^(n) ge 1 + nx. whenever x is p...

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  13. Prove that 3^(2n)-1 is divisible by 8.

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  14. Prove that x^n-y^n is divisible by x - y for all positive integers n.

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  15. Prove by mathematical induction that for every natural number n, 3^(2n...

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  16. Use the principle of mathematical induction to prove that for every na...

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  17. n^(3)-n is divisible by 6, for each natural number n ge 2

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  18. Prove that For any natural number n, 7^n - 2^n is divisible by 5.

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  19. Find (10!)/(5!" X "2!)

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