Question Number 157074 by amin96 last updated on 19/Oct/21
$$\sqrt{\mathrm{4}+\sqrt{\mathrm{4}^{\mathrm{2}} +\sqrt{\mathrm{4}^{\mathrm{3}} +\sqrt{\mathrm{4}^{\mathrm{4}} +\ldots}}}}=? \\ $$
Answered by MJS_new last updated on 19/Oct/21
$$\mathrm{3} \\ $$
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
$$\:\:\:\:\:\:\mathrm{a}+\mathrm{2}=\sqrt{\mathrm{4}+\mathrm{a}\sqrt{\mathrm{16}+\mathrm{a}\sqrt{\mathrm{64}+\mathrm{a}\sqrt{\mathrm{256}+.....}}}} \\ $$$$\:\:\:\:\:\:\mathrm{a}=\mathrm{1}\Leftrightarrow\mathrm{3}=\sqrt{\mathrm{4}+\sqrt{\mathrm{16}+\sqrt{\mathrm{64}+\sqrt{\mathrm{256}+...}}}} \\ $$