Question

Determine os 5 primeiros termos da sequencia a seguir A) an=(1+1/n)^n

Answer 1

Olá,
basta substituir n, por cada termo, assim:

$a_n=\left(1+ \dfrac{1}{n}\right)^n\\\\\\ para~n=1\Rightarrow a_1=\left(1+ \dfrac{1}{1}\right)^1=(1+1)^1=2^1=2\\\\ para~n=2\Rightarrow a_2=\left(1+ \dfrac{1}{2}\right)^2= \left(\dfrac{3}{2}\right)^2= \dfrac{9}{4}\\\\ para~n=3\Rightarrow a_3=\left(1+ \dfrac{1}{3}\right)^3=\left( \dfrac{4}{3}\right)^3= \dfrac{64}{27}\\\\ para~n=4\Rightarrow a_4=\left(1+ \dfrac{1}{4}\right)^4=\left( \dfrac{5}{4}\right)^4= \dfrac{625}{256}$

$para~n=5\Rightarrow a_5=\left(1+ \dfrac{1}{5}\right)^5=\left( \dfrac{6}{5}\right)^5= \dfrac{7.776}{3.125}$

Sendo assim, os cinco primeiros termos são eles..

$~a_1~~a_2~~a_3~~~a_4~~~~~a_5\\~~~|~~~~|~~~~|~~~~~|~~~~~~~|\\\left(2,~ \dfrac{9}{4} ,~ \dfrac{64}{27}~ \dfrac{625}{256},~ \dfrac{7.776}{3.125}\right)$

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