Ensino Fundamental ⇒ Raízes Tópico resolvido

[IRONMAN]

Determine [tex3]n[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]n[/tex3]

se

[tex3]\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{n}+\sqrt{n+1}}=10[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{n}+\sqrt{n+1}}=10[/tex3]

Resposta

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n=120

[MatheusBorges]

Fala frango kkkk
[tex3]\frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{\sqrt{n}-\sqrt{n+1}}{\sqrt{n}^{2}-(\sqrt{n+1})^{2}}=\sqrt{n+1}-\sqrt{n}\\
\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\sqrt{5}-\sqrt{4}+....+\sqrt{n+1}-\sqrt{n}=11\\
-1+\sqrt{n+1}=11\\
n+1=121\\
n=120[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{\sqrt{n}-\sqrt{n+1}}{\sqrt{n}^{2}-(\sqrt{n+1})^{2}}=\sqrt{n+1}-\sqrt{n}\\
\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\sqrt{5}-\sqrt{4}+....+\sqrt{n+1}-\sqrt{n}=11\\
-1+\sqrt{n+1}=11\\
n+1=121\\
n=120[/tex3]

[IRONMAN]

Fala frango kkkk
[tex3]\frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{\sqrt{n}-\sqrt{n+1}}{\sqrt{n}^{2}-(\sqrt{n+1})^{2}}=\sqrt{n+1}-\sqrt{n}\\
\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\sqrt{5}-\sqrt{4}+....+\sqrt{n+1}-\sqrt{n}=11\\
-1+\sqrt{n+1}=11\\
n+1=121\\
n=120[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{\sqrt{n}-\sqrt{n+1}}{\sqrt{n}^{2}-(\sqrt{n+1})^{2}}=\sqrt{n+1}-\sqrt{n}\\
\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\sqrt{5}-\sqrt{4}+....+\sqrt{n+1}-\sqrt{n}=11\\
-1+\sqrt{n+1}=11\\
n+1=121\\
n=120[/tex3]

Valeu chefe....AHAHAHAHAH bem burro mais bem forte

[IRONMAN]

Fala frango kkkk
[tex3]\frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{\sqrt{n}-\sqrt{n+1}}{\sqrt{n}^{2}-(\sqrt{n+1})^{2}}=\sqrt{n+1}-\sqrt{n}\\
\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\sqrt{5}-\sqrt{4}+....+\sqrt{n+1}-\sqrt{n}=11\\
-1+\sqrt{n+1}=11\\
n+1=121\\
n=120[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{\sqrt{n}-\sqrt{n+1}}{\sqrt{n}^{2}-(\sqrt{n+1})^{2}}=\sqrt{n+1}-\sqrt{n}\\
\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\sqrt{5}-\sqrt{4}+....+\sqrt{n+1}-\sqrt{n}=11\\
-1+\sqrt{n+1}=11\\
n+1=121\\
n=120[/tex3]

Não seria [tex3]\sqrt{n+1}-1= 10 \rightarrow \sqrt{n+1} = 11 \rightarrow n=120 ?

Pq -1 + \sqrt{n+1} = 11 \rightarrow n= 143[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\sqrt{n+1}-1= 10 \rightarrow \sqrt{n+1} = 11 \rightarrow n=120 ?

Pq -1 + \sqrt{n+1} = 11 \rightarrow n= 143[/tex3]

[NathanMoreira]

Sim, você está correto.

[tex3]\sqrt{n+1}-1= 10 \rightarrow \sqrt{n+1} = 11 \rightarrow n=120[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\sqrt{n+1}-1= 10 \rightarrow \sqrt{n+1} = 11 \rightarrow n=120[/tex3]