Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If the Sum of First N Even Natural Numbers is Equal to K Times the Sum of First N Odd Natural Numbers, Then K = - Mathematics

MCQ

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =

Options

  • \[\frac{1}{n}\]

  • \[\frac{n - 1}{n}\]

  • \[\frac{n + 1}{2n}\]

  • \[\frac{n + 1}{n}\]

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Solution

\[\frac{n + 1}{n}\]

Given:
Sum of the even natural numbers = k\[\times\] Sum of the odd natural numbers

\[\frac{n}{2}\left\{ 2a + \left( n - 1 \right)d \right\} = k \times \frac{n}{2}\left\{ 2a + \left( n - 1 \right)d \right\}\]

\[ \Rightarrow \left\{ 2 \times 2 + \left( n - 1 \right)2 \right\} = k \times \left\{ 2 \times 1 + \left( n - 1 \right)2 \right\}\]

\[ \Rightarrow \frac{4 + \left( n - 1 \right)2}{2 + \left( n - 1 \right)2} = k\]

\[ \Rightarrow \frac{n + 1}{n} = k\]

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Q 17 | Page 52
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