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Using the principle of mathematical induction. Prove that `(x^(n)-y^(n))` is divisible by `(x-y)` for all ` n in N`.

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RD SHARMA ENGLISH-MATHEMATICAL INDUCTION-All Questions
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  3. Using the principle of mathematical induction. Prove that (x^(n)-y^(n...

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  8. Prove that: 1^2+2^2+3^2.....+n^2>(n^3)/3,n in N

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  11. Prove by the principle of mathematical induction that for all n in N ...

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  13. Prove the following by using the principle of mathematical inductio...

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  14. Prove that: (1+1/1)(1+1/2)(1+1/3)(1+1/n)=(n+1) for all n in Ndot

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  17. For all positive integer n , prove that (n^7)/7+(n^5)/5+2/3n^3-n/(105)...

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  20. If P(n) is the statement n^2&gt; 100" , prove that whenever P(r) is...

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