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For each n in N, the correct statement i...

For each `n in N,` the correct statement is

A

`2^n lt n`

B

`n^2 lt 2n`

C

`n^4 lt 10^n`

D

`2^(3n) gt 7n +1`

Text Solution

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The correct Answer is:
C
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DISHA PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-Exercise-1 Concept Builder
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  2. Principle of mathematical induction is used

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  3. For each n in N, the correct statement is

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  4. If n is a natural number then ((n+1)/2)^n ge n! is true when

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  5. For natural number n , 2^n (n-1)!lt n^n , if

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  6. If P(n):2nltn!,ninN then P(n) is true for all le . . . . . . . . . .

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  7. If 4^n/(n+1) lt ((2n)!)/((n!)^2), then P(n) is true for

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  8. For every positive integral value of n, 3 ^(n) gt n^(3) when

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  9. If x gt -1 , then the statement (1+x)^n gt 1 +nx is true for

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  10. For all positive integral values of n, 3^(2n)-2n+1 is divisible by

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  11. For every natural number n, n(n^2-1) is divisible by

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  14. 10^n+3(4^(n+2))+5 is divisible by (n in N)

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  18. The greatest positive integer , which divides (n+1)(n+2)(n+3)…(n+r) fo...

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