2-4-8-16-32-pls-help-

Question Number 119138 by 675480065 last updated on 22/Oct/20

\sqrt{2 \sqrt{4 \sqrt{8 \sqrt{16 \sqrt{32 \dots}}}}} = ?

pls help

Commented by Dwaipayan Shikari last updated on 22/Oct/20

4 = \sqrt{2.8}

4 = \sqrt{2 \sqrt{64}}

4 = \sqrt{2 \sqrt{4 \sqrt{256}}}

4 = \sqrt{2 \sqrt{4 \sqrt{8 \sqrt{1024}}}}

4 = \sqrt{2 \sqrt{4 \sqrt{8 \sqrt{16 \sqrt{32 \sqrt{32^{2} . 64^{2} \dots} \dots}}}}}

\sqrt{2 \sqrt{4 \sqrt{8 \sqrt{16 \sqrt{32 \dots}}}}} = 4

Answered by PRITHWISH SEN 2 last updated on 22/Oct/20

n^{2} = \sqrt{n . n^{3}} = \sqrt{n . \sqrt{n^{6}}} = \sqrt{n . \sqrt{n^{2} n^{4}}} = \sqrt{n . \sqrt{n^{2} . \sqrt{n^{16}}}}

= \sqrt{n . \sqrt{n^{2} . \sqrt{n^{3} \sqrt{n^{4} . \sqrt{n^{5} \dots}}}}}

n = 2

4 = \sqrt{2 \sqrt{4 \sqrt{8 \sqrt{16 \dots . .}}}}

n = 3

9 = \sqrt{3 \sqrt{9 \sqrt{27 \sqrt{81 \dots . .}}}}

\dots \dots \dots