Question

b1= 1/4

bn+1=(bn)^2 x 4^n
oblicz b5
ma wyjść 4 do 10

Answer 1

[tex]b_1=\dfrac{1}{4}[/tex]

[tex]b_{n+1}=(b_n)^2\cdot4^n[/tex]

[tex]b_2=(b_1)^2\cdot4^1=\left(\dfrac{1}{4}\right)^2\cdot4^1=\dfrac{1}{16}\cdot4=\dfrac{1}{4}[/tex]

[tex]b_3=(b_2)^2\cdot4^2=\left(\dfrac{1}{4}\right)^2\cdot4^2=\dfrac{1}{16}\cdot16=1[/tex]

[tex]b_4=(b_3)^2\cdot4^3=1^2\cdot4^3=1\cdot4^3=4^3[/tex]

[tex]b_5=(b_4)^2\cdot4^4=(4^3)^2\cdot4^4=4^6\cdot4^4=4^{10}[/tex]