If 10n + 3.4n+2 + k is divisible by 9 for all n ∈ N, then the least positive integral value of k is ______.

प्रश्न

If 10ⁿ + 3.4ⁿ⁺² + k is divisible by 9 for all n ∈ N, then the least positive integral value of k is ______.

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MCQ

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उत्तर

If 10ⁿ + 3.4ⁿ⁺² + k is divisible by 9 for all n ∈ N, then the least positive integral value of k is 5.

Explanation:

Let P(n) = 10ⁿ + 3.4^{n + 2} + k is divisible by 9, ∀ n ∈ N

P(1) = 10¹ + 3.4^{1 + 2} + k = 10 + 3.64 + k

= 10 + 192 + k = 202 + k must be divisible by 9.

If (202 + k) is divisible by 9 then k must be equal to 5.

202 + 5 = 207 which is divisible by 9.

= `207/9`

= 23

So, the least positive integral value of k = 5.

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Principle of Mathematical Induction

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Q 26 Q 25 Q 27

अध्याय 4: Principle of Mathematical Induction - Exercise [पृष्ठ ७२]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11

अध्याय 4 Principle of Mathematical Induction
Exercise | Q 26 | पृष्ठ ७२

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Principle of Mathematical Induction

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