Find the value of the following:
^@1 + \dfrac { 1 } { 1 + \dfrac {1} { 2 } }^@


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Answer:

^@\dfrac { 5 } { 3 }^@

Step by Step Explanation:
  1. ^@1 + \dfrac { 1 } { 1 + \dfrac {1} { 2 } }^@ can be simplified as:
    ^@ \begin {align} 1 + \dfrac {1} { \dfrac { 2 + 1 } { 2 } } \\ = 1 + \dfrac {1} { \dfrac { 3 } { 2 } } \\ = 1 + \dfrac { 2 } { 3 } \\ = \dfrac { 3 + 2 } { 3 } \\ = \dfrac { 5 } { 3 }\end {align}^@
  2. Therefore, the value of ^@1 + \dfrac { 1 } { 1 + \dfrac {1} { 2 } }^@ is ^@\dfrac { 5 } { 3 }^@.

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