Can someone please explain i’m confused
2 answers:
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I believe the answer is the first one ! Keep in your mind that the first part of the ordered pair is always the domain , and the second part of the ordered pair is the range !!
Don’t forget a brainliest if this helped ;)
Don’t forget a brainliest if this helped ;)
Answer:
See proof below
Step-by-step explanation:
Let L be the limit of Xn when n goes to infinity. We will use the recursive formula for the Fibonacci numbers to find L. Bur first, we need to guarantee that our operations with the formula make sense:
Notice that Fn>0 for all n≥0. Then Fn+2 = Fn+1 + Fn > Fn+1. Hence, dividing by Fn+1, Xn+1= Fn+2/Fn+1 > 1 for all n≥0, that is, Xn>1 for all n≥1. Taking the limit on both sides of the inequality, L≥1,, thus 1/L exists and equal the limit of the sequence 1/Xn=Fn/Fn+1 (by laws of limits).
To find L, divide by Fn+1 in Fn+2 = Fn + Fn+1 to get
Fn+2/Fn+1 = Fn/Fn+1 +1.
This equation can be written as Xn+1= 1/Xn +1. Take the limit in both sides to get L=1/L +1. Then L²=1+L, and L²-L-1=0,
Solve for L with the quadratic formula to get:
We discard the second solution because it is negative, and we proved above that L>0. Hence