Question Number 207085 by necx122 last updated on 06/May/24

Answered by A5T last updated on 06/May/24
![f(2n)=nf(n) f(n)=(n/2)f((n/2))=(n/2)×(n/4)f((n/4)) =(n^q /2^(1+2+3+...+q) )f((n/2^q )) [by induction] ⇒f(2^(10) )=(((2^(10) )^(10) )/2^(1+2+3+...+10) )f((2^(10) /2^(10) ))=(2^(100) /2^(55) )=2^(45)](https://www.tinkutara.com/question/Q207086.png)
Commented by A5T last updated on 06/May/24
![f(2^(10) )=f(2×2^9 )=2^9 ×f(2^9 )=2^9 ×[2^8 ×f(2^8 )] =2^(9+8) ×2^7 f(2^7 )=2^(9+8+7+...+3) ×2^2 f(2^2 ) =2^(9+8+7+...+2) ×2f(2)=2^(45)](https://www.tinkutara.com/question/Q207090.png)
Commented by necx122 last updated on 06/May/24

Commented by necx122 last updated on 06/May/24

Answered by A5T last updated on 06/May/24
