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

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Question

(c) Let ${S_{Even}} = 2 + 4 + 6 + 8 + ........\infty $ &hellip;..$(i)$

and ${S_{Odd}} = 1 + 3 + 5 + 7 + 9 + .......\infty $ &hellip;..$(ii)$

${S

Vedclass · Accepted Answer

$(n + 1):n$

Vedclass · Answer

(c) Let ${S_{Even}} = 2 + 4 + 6 + 8 + ........\infty $ &hellip;..$(i)$

and ${S_{Odd}} = 1 + 3 + 5 + 7 + 9 + .......\infty $ &hellip;..$(ii)$

${S_E} = \frac{n}{2}[4 + (n - 1)2] = \frac{n}{2}(2n + 2) = n(n + 1)$

${S_O} = \frac{n}{2}[2 + (n - 1)2] = \frac{n}{2}(2n)$

Now $\frac{{{S_E}}}{{{S_O}}} = \frac{{(n + 1)}}{n}$

or ${S_E}:{S_O} = (n + 1):n$.

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

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