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Question Number 157074 by amin96 last updated on 19/Oct/21

(√(4+(√(4^2 +(√(4^3 +(√(4^4 +…))))))))=?

$$\sqrt{\mathrm{4}+\sqrt{\mathrm{4}^{\mathrm{2}} +\sqrt{\mathrm{4}^{\mathrm{3}} +\sqrt{\mathrm{4}^{\mathrm{4}} +\ldots}}}}=? \\ $$

Answered by MJS_new last updated on 19/Oct/21

3

$$\mathrm{3} \\ $$

Commented by amin96 last updated on 19/Oct/21

????

$$???? \\ $$

Commented by MJS_new last updated on 19/Oct/21

!!!!

$$!!!! \\ $$

Answered by Javokhir last updated on 19/Oct/21

      a+2=(√(4+a(√(16+a(√(64+a(√(256+.....))))))))        a=1⇔3=(√(4+(√(16+(√(64+(√(256+...))))))))

$$\:\:\:\:\:\:\mathrm{a}+\mathrm{2}=\sqrt{\mathrm{4}+\mathrm{a}\sqrt{\mathrm{16}+\mathrm{a}\sqrt{\mathrm{64}+\mathrm{a}\sqrt{\mathrm{256}+.....}}}} \\ $$$$\:\:\:\:\:\:\mathrm{a}=\mathrm{1}\Leftrightarrow\mathrm{3}=\sqrt{\mathrm{4}+\sqrt{\mathrm{16}+\sqrt{\mathrm{64}+\sqrt{\mathrm{256}+...}}}} \\ $$

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