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Ancaiordache66
a fost răspuns

Numarul natural ''x'' ce verifica egalitatea:
1*6+5*6+5*6²+5*6³+...+5*6²⁰¹⁹ totul sub radical=36¹⁰¹ˣ
Multumesc anticipat!

Răspuns :

Razzvy
O sa fac suma fara radical mai intai:

[tex]S = 6 + 5(6^{1}+6^{2}+6^{3}+...+6^{2010})\\ S_{1}=6^{1}+6^{2}+6^{3}+...+6^{2010}[/tex]

Inmultim S1 cu 6:

[tex]6S_{1}=6^{2}+6^{3}+6^{4}+...+6^{2010}+6^{2011}\\ 6S_{1}=S_{1}-6^{1}+6^{2011}\\ 5S_{1}=6^{2011}-6\\ S_{1}= \frac{6^{2011}-6}{5} \\\\ S=6+5S_{1}=6+6^{2011}-6=6^{2011}[/tex]
[tex] \sqrt{S}= \sqrt{6^{2011}} = \sqrt{36^{ \frac{2011}{2} }} = 36^{ \frac{2011}{4} } \rightarrow \frac{2011}{4}=101x\\ x= \frac{2011}{404} [/tex]

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