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The distributive law from algebra states...

The distributive law from algebra states that for all real numbers c,a1 and a2,we have `c(a_1+a_2)=c a_1+c a_2` Use this law and mathematical induction to prove that,for all natural numbers,`ngeq2`,if `c,a_1,a_2,....,`an are any real numbers,then `c(a_1+a_2+.....+a_n)=c a_1+c a_2+....+c a_n`

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

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

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

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

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

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

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  11. State First principle of mathematical induction

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

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

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

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

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

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  18. Let P(n):2^n<(1xx2xx3xxxxn) . Then the smallest positive integer for w...

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  19. A student was asked to prove a statement by induction. He proved (i) P...

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  20. If P(n): 49^n+16^n+lambda is divisible by 64 for n in N is true, then ...

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