Let A 0 </msub> = <mstyle displaystyle="true" scriptlevel="0">

Ayaan Barr

Ayaan Barr

Answered question

2022-07-07

Let A 0 = 3 4 , and A n + 1 = 1 + A n 2 for all n 0
How to find the value of n = 1 A n ?

Answer & Explanation

cefflid6y

cefflid6y

Beginner2022-07-08Added 13 answers

If we set A n = cos 2 ( θ n ), we get:
A n + 1 = 1 + cos ( θ n ) 2 = cos 2 ( θ n 2 ) ,
and since θ 0 = π 6 , induction gives:
A n = cos 2 ( π 6 2 n ) = ( sin ( π 6 2 n 1 ) 2 sin ( π 6 2 n ) ) 2
from which it follows that:
n = 1 + A n = ( 3 π ) 2 = 9 π 2 .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?