The sum of 24 terms of the following series s | vedclass

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(B) The given series is $\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + \dots$This can be rewritten as $1\sqrt 2 + 2\sqrt 2 + 3\sqrt 2 + 4\sqrt 2 + \do

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$300\sqrt 2 $

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(B) The given series is $\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + \dots$This can be rewritten as $1\sqrt 2 + 2\sqrt 2 + 3\sqrt 2 + 4\sqrt 2 + \dots$This is an arithmetic progression where the first term $a = \sqrt 2$ and the common difference $d = \sqrt 2$.The sum of $n$ terms of an arithmetic progression is given by $S_n = \frac{n}{2} [2a + (n - 1)d]$.For $n = 24$ terms:$S_{24} = \frac{24}{2} [2(\sqrt 2) + (24 - 1)\sqrt 2]$$S_{24} = 12 [2\sqrt 2 + 23\sqrt 2]$$S_{24} = 12 [25\sqrt 2]$$S_{24} = 300\sqrt 2$.

The sum of $24$ terms of the following series $\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + \dots$ is

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