Find the sum:4-frac{1}{n}+4-frac{2}{n}+4-frac | vedclass

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(C) The given series is $4-\frac{1}{n}, 4-\frac{2}{n}, 4-\frac{3}{n}, \ldots$ up to $n$ terms.This is an Arithmetic Progression $(AP)$ where the first

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$\frac{7n-1}{2}$

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(C) The given series is $4-\frac{1}{n}, 4-\frac{2}{n}, 4-\frac{3}{n}, \ldots$ up to $n$ terms.This is an Arithmetic Progression $(AP)$ where the first term $a = 4 - \frac{1}{n}$.The common difference $d = (4 - \frac{2}{n}) - (4 - \frac{1}{n}) = -\frac{2}{n} + \frac{1}{n} = -\frac{1}{n}$.The sum of $n$ terms of an $AP$ is given by $S_n = \frac{n}{2}[2a + (n-1)d]$.Substituting the values of $a$ and $d$:$S_n = \frac{n}{2} [2(4 - \frac{1}{n}) + (n-1)(-\frac{1}{n})]$$S_n = \frac{n}{2} [8 - \frac{2}{n} - 1 + \frac{1}{n}]$$S_n = \frac{n}{2} [7 - \frac{1}{n}]$$S_n = \frac{n}{2} [\frac{7n-1}{n}]$$S_n = \frac{7n-1}{2}$.

Find the sum:
$4-\frac{1}{n}+4-\frac{2}{n}+4-\frac{3}{n}+\ldots$ up to $n$ terms.

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Find the sum:$4-\frac{1}{n}+4-\frac{2}{n}+4-\frac{3}{n}+\ldots$ up to $n$ terms.