B1= 1/4bn+1=(bn)^2 x 4^noblicz b5ma wyjść 4 do 10

February 01, 2022

B1= 1/4

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

$b_1=\dfrac{1}{4}$

$b_{n+1}=(b_n)^2\cdot4^n$

$b_2=(b_1)^2\cdot4^1=\left(\dfrac{1}{4}\right)^2\cdot4^1=\dfrac{1}{16}\cdot4=\dfrac{1}{4}$

$b_3=(b_2)^2\cdot4^2=\left(\dfrac{1}{4}\right)^2\cdot4^2=\dfrac{1}{16}\cdot16=1$

$b_4=(b_3)^2\cdot4^3=1^2\cdot4^3=1\cdot4^3=4^3$

$b_5=(b_4)^2\cdot4^4=(4^3)^2\cdot4^4=4^6\cdot4^4=4^{10}$