A sequence is defined as a1 = a2 = 1 and an = an-1 + an-2 for all n ≥ 3 then
{ an } is an increasing sequence TRUE / FALSE
106This is Fibonacci sequence .. the terms are increasing
1,1,2,3,5,8,13,21,....
proof:
all terms are positive..
an > an-1 (as all terms are positive and an = a(n-1) + a(n-2) )
=> the next term is greater than the previous term hence the sequence is increasing
341Its like this, they want you to prove that every term is +ve which is easily done by strong induction
106sir as any term is the sum of its previous terms..
and the first two terms are positive .. then wont all terms be positive..
(as it is given true/false question) i did not bother about induction..
But sir isnt this a bit too obvious for induction (i mean it is clearly the fibonacci series isnt it)?
341Ya, the qn is ill-framed that way. The idea is to argue from fundamentals rather than from known facts. But using the Fibonacci recursion is bad judgement from the question setter.
62@Prophet Sir: I wonder how many ppl i know understand "mathematics" as well as you do [1]
