huh? Just plug in the values for n...
a_1 = 1
a_2 = (a_1 + 1)/a_1 = (1+1)/1 = 2
a_3 = (a_2 + 1)/a_2 = (2+1)/2 = 3/2
and so on
List the first five terms of the sequence given by a_1 = 1, a_(n+1) = (a_n +1) / a_n
_ = Subscript
4 answers
Ok, Thank you. So, 1,2,3/2, 4/3, 5/4, 6/5?
no. you just guessed, instead of calculating!
a_4 = (3/2 + 1) / (3/2) = 5/2 / 3/2 = 5/3
a_4 = (3/2 + 1) / (3/2) = 5/2 / 3/2 = 5/3
I hope you were as surprised and pleased as I was, when I noticed that for each a_n, the numerator and denominator are consecutive Fibonacci Numbers F_n/F_(n+1) !