Find a recursive formula for I n </msub> = <msubsup> &#x222B;<!-- ∫ --> 0

Montenovofe

Montenovofe

Answered question

2022-07-07

Find a recursive formula for I n = 0 2 x n ( 4 x 2 ) 1 / 2 d x

Answer & Explanation

Sariah Glover

Sariah Glover

Beginner2022-07-08Added 16 answers

Let
A n = 0 2 d x   x n ( 4 x 2 ) 1 / 2
then
I n = 4 A n A n + 2
4 n A n 1 = ( n + 3 ) A n + 1
Now, we use this relation to relate I n 1 and I n + 1
I n + 1 = 4 A n + 1 A n + 3
I n 1 = 4 A n 1 A n + 1 Eliminating A n + 3 and A n 1 , we get
I n 1 = 3 n A n + 1
and
I n + 1 = 12 n + 5 I n + 1
Diving these you get
( n + 5 ) I n + 1 = 4 n I n 1
I am not sure if your relation ( n + 3 ) I n + 1 = 4 n I n 1 is correct.

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