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What will come in place of question mark in the following series? \(\frac{1}{2},\;1,\;1\frac{1}{2},\;2,\;2\frac{1}{2},\;3,\;?\)

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What will come in place of question mark in the following series?

\(\frac{1}{2},\;1,\;1\frac{1}{2},\;2,\;2\frac{1}{2},\;3,\;?\)


1). \(3\frac{1}{2}\)
2). \(2\frac{1}{3}\)
3). 4
4). \(3\frac{1}{4}\)


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The given series is,

$(\begin{array}{l} \to \frac{1}{2},\\ \to 1 = \frac{1}{2}\; + \frac{1}{2},\\ \to 1\frac{1}{2}\; = \;1\; + \frac{1}{2},\\ \to 2 = 1\frac{1}{2} + \frac{1}{2},\;\\ \to 2\frac{1}{2} = 2 + \frac{1}{2},\\ \to 3 = 2\frac{1}{2} + \frac{1}{2},\\ \to {\rm{\;}}? = 3 + \frac{1}{2} = 3\frac{1}{2} \end{array})$

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