Question

fie functia f:(0,+ infinit)-->R,f(x)=log baza 2 din x.Sa se calculeze suma : S=f(1/2)+f(2/3)+f(3/4)+...+f(63/64)​

Answer 1

Răspuns:

$\log_2\dfrac{1}{2}+\log_2\dfrac{2}{3}+\ldots+\log_2\dfrac{63}{64}=\log_2\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\ldots\cdot\dfrac{63}{64}\right)=\\=\log_2\dfrac{1}{64}=\log_22^{-6}=-6$

Explicație pas cu pas: