Find the n^{th} term of the series:frac{1}{n} | vedclass

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(B) The given series is an Arithmetic Progression $(AP)$ where the first term $a = \frac{1}{n}$.The common difference $d$ is calculated as:$d = \frac{

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$\frac{1+n^{2}-n}{n}$

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(B) The given series is an Arithmetic Progression $(AP)$ where the first term $a = \frac{1}{n}$.The common difference $d$ is calculated as:$d = \frac{n+1}{n} - \frac{1}{n} = \frac{n+1-1}{n} = \frac{n}{n} = 1$.The formula for the $n^{th}$ term of an $AP$ is $a_n = a + (n-1)d$.Substituting the values:$a_n = \frac{1}{n} + (n-1)(1)$$a_n = \frac{1}{n} + n - 1$$a_n = \frac{1 + n(n-1)}{n}$$a_n = \frac{1 + n^2 - n}{n}$.

Find the $n^{th}$ term of the series:
$\frac{1}{n} + \frac{n+1}{n} + \frac{2n+1}{n} + \ldots$

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Find the $n^{th}$ term of the series:$\frac{1}{n} + \frac{n+1}{n} + \frac{2n+1}{n} + \ldots$