Question

Se considera sirul 1/3;3/5;7/9;15/17...... Fractia aflata pe pozitia 100 in sir este:

Va rog e urgent!!!!!!!!!​
Cu rezolvare completa!!!!!!!!!!!

Answer 1

dupa cum poti observa,formula generala este (2ⁿ-1)/(2ⁿ+1) unde n este pozitia fractiei in sir.asadar al 100-lea termen este:

(2¹⁰⁰-1)/(2¹⁰⁰+1)=((2²)⁵⁰-1)/((2²)⁵⁰+1)=(4⁵⁰-1)/(4⁵⁰+1)=>b)

Answer 2

$\it f_1=\dfrac{1}{3}=\dfrac{2^1-1}{2^1+1}\\ \\ \\ f_2=\dfrac{3}{5}=\dfrac{2^2-1}{2^2+1}\\ \\ \\ f_3=\dfrac{7}{9}=\dfrac{2^3-1}{2^3+1}\\ \\ \vdots\\ \\ f_{100}=\dfrac{2^{100}-1}{2^{100}+1}=\dfrac{(2^2)^{50}-1}{(2^2)^{50}+1}=\dfrac{4^{50}-1}{4^{50}+1}$