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Prove the following by the principle of mathematical induction: `7+77+777++777++\ ddotn-d igi t s7=7/(81)(10^(n+1)-9n-10)` for all `n in N `

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RD SHARMA ENGLISH-MATHEMATICAL INDUCTION-All Questions
  1. Prove the following by the principle of mathematical induction: n^3...

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  2. Prove the following by the principle of mathematical induction:\ 1+2...

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  3. Prove the following by the principle of mathematical induction: 7+77...

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  4. Prove the following by the principle of mathematical induction: (n^7...

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  5. Prove the following by the principle of mathematical induction:(n^(1...

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  6. Prove the following by the principle of mathematical induction: 1/2tan...

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  7. Prove the following by the principle of mathematical induction: (1-1...

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  8. Prove the following by the principle of mathematical induction: ((2...

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  9. Prove the following by the principle of mathematical induction: \ x^...

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  10. Prove that: \ sin x+sin3x++sin(2n-1)x=(sin^2\ \ n x)/(sin x) for all n...

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  11. Given a1=1/2(a0+A/(a0)), a2=1/2(a1+A/(a1)) and a(n+1)=1/2(an+A/(an)) ...

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  12. Let P(n) be the statement: 2^n >= 3n. If P(r) is true, show that P (r...

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  13. The distributive law from algebra states that for all real numbers c,a...

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  14. State First principle of mathematical induction

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  15. Write the set of values of n for which the statement P(n):2n < n! is t...

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  16. Let us prove the following equality using the second principle: For an...

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  17. If P(n):2xx4^(2n+1)-3^(3n+1) is divisible bylambda for all n in N is t...

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  18. If x^n-1 is divisible by x-lambda, then the least prositive integral v...

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  19. For all n in N , 3xx5^(2n+1)+2^(3n+1) is divisible by a.19 b. 17 c. 23...

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  20. If 10^n+3xx4^(n+2)+lambda is divisible by 9 or all natural numbers, t...

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