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Applications of Dot Product

The A.M. of f...

Question

The A.M. of first n even natural number is

n (n + 1)

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\frac{n + 1}{2}

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\frac{n}{2}

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n + 1

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Solution

The correct option is D $n + 1$
$A . M . = \frac{2 + 4 + . . . . . + 2 n}{n} = \frac{2 (1 + 2 + . . . . . + n)}{n} = \frac{2 n (n + 1)}{2 n} = n + 1$
Ans: D

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Prove that: 1 + 2 + 3 + ......... + n = $\frac{n (n + 1)}{2}$ i.e., the sum of the first n natural numbers is $\frac{n (n + 1)}{2}$ .

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

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