Another nested radical

Algebra Level 4

2⋅82+2⋅84+2⋅88⋯=a\sqrt { 2\cdot 8^{ 2 }+\sqrt { 2\cdot 8^{ 4 }+\sqrt { 2\cdot 8^{ 8 }\cdots} } } =a

Find a2\dfrac{a}{2}.

Bonus:Generalize it.

Hamza A by Hamza A
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