Question

5/6, 7/11, 10/18, 15/28, 22/43, ?

Answer 1

HI,

33/65

Explanation:

P={2,3,5,7,11,13,17,19,23,29,31,37,41,43,...}= x is a prime number

P(1)=2, P(2)=3,P(3)=5,P(4)=7,...

`u_1=(5)/(6) \\\\u_2=(5+P(1))/(5+6) =(5+2)/(11)=(7)/(11) \\\\u_3=(7+P(2))/(7+11) =(7+3)/(18) =(10)/(18)\\\\u_4=(10+P(3))/(10+18) =(10+5)/(28)=(15)/(28) \\\\u_5=(15+P(4))/(15+28) =(15+7)/(43)=(22)/(43) \\\\u_6=(22+P(5))/(22+43) =(22+11)/(65)=\boxed{(33)/(65) }\\\\\\\boxed{u_(n+1)=(num(u_n)+P(n) )/(num(u_n)+den(u_n)) }\\\\\\u_n=(num(u_n))/(den(u_n))`