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Integration by Parts Recurrence stuff.. :S (1 Viewer)

Dumsum

Dumsum

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Am I overlooking something simple? Say there's a statement like:
I<sub>n</sub> = (n - 1)(I<sub>n-2</sub> - I<sub>n</sub>)

And they go straight from that to:
Hence I<sub>n</sub> = (n - 1)/n . I<sub>n-2</sub>

What is actually going on? Me = confuzzled.


(not sure if relevant)
I<sub>n</sub> = (integral 0 -> pi/2) cos<sup>n</sup>x.dx
 
ngai

ngai

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Dumsum said:
Am I overlooking something simple? Say there's a statement like:
I<sub>n</sub> = (n - 1)(I<sub>n-2</sub> - I<sub>n</sub>)

And they go straight from that to:
Hence I<sub>n</sub> = (n - 1)/n . I<sub>n-2</sub>

What is actually going on? Me = confuzzled.


(not sure if relevant)
I<sub>n</sub> = (integral 0 -> pi/2) cos<sup>n</sup>x.dx
Click to expand...
using A and B instead of In and In-2
A = (n-1)(B-A)
= (n-1)B - (n-1)A
= (n-1)B - nA + A
0 = (n-1)B - nA
nA = (n-1)B
A = (n-1)/n B
 
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