The ratio of the sums of the first n even num | vedclass

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Question

(C) The sum of the first $n$ even numbers is given by the formula $S_{Even} = 2 + 4 + 6 + \dots + 2n = n(n + 1)$.The sum of the first $n$ odd numbers

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$(n + 1):n$

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(C) The sum of the first $n$ even numbers is given by the formula $S_{Even} = 2 + 4 + 6 + \dots + 2n = n(n + 1)$.The sum of the first $n$ odd numbers is given by the formula $S_{Odd} = 1 + 3 + 5 + \dots + (2n - 1) = n^2$.Therefore,the ratio of the sum of the first $n$ even numbers to the sum of the first $n$ odd numbers is $\frac{S_{Even}}{S_{Odd}} = \frac{n(n + 1)}{n^2} = \frac{n + 1}{n}$.Thus,the ratio is $(n + 1):n$.

The ratio of the sums of the first $n$ even numbers and $n$ odd numbers is

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