Question Number 56851 by behi83417@gmail.com last updated on 25/Mar/19
![let: [u_n =(√u_(n−1) )+(√u_(n−2) ),u_0 =1,u_1 =1] ⇒ Σ_0 ^∞ ((1/u_n ))=?](Q56851.png)
$${let}:\:\left[\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}} =\sqrt{\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}−\mathrm{1}} }+\sqrt{\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}−\mathrm{2}} },\boldsymbol{\mathrm{u}}_{\mathrm{0}} =\mathrm{1},\boldsymbol{\mathrm{u}}_{\mathrm{1}} =\mathrm{1}\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\underset{\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}} }\right)=? \\ $$