Proving a relation in integration

A

Appot89

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Jul 10, 2020
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4
L(n)= CodeCogsEqn (1).gif
1) Calculate L(0): I got 2/3
2) Calculate L(1) using integration by parts: I got 4/15
3) Show that for every natural number n of (2n+3)*L(n)=2*n*L(n-1). Please help me on solving this problem. I tried using integration by parts but could not prove this statement..

1594474362928.png[added later]
 
Appot89 said:
L(n)= View attachment 20365
1) Calculate L(0): I got 2/3
2) Calculate L(1) using integration by parts: I got 4/15
3) Show that for every natural number n of (2n+3)*L(n)=2*n*L(n-1). Please help me on solving this problem. I tried using integration by parts but could not ptove this statement..
Click to expand...
First, write an expression for L(n-1).
 
Hi,
It is not fair for you to want us to validate your answer without you showing us your work. The reason is that we would have to workout the integral ourselves and if we do not get your answer then we can't even tell you where you made your mistake. We just want to help you the best we can. So please post back with your work. Thank you.
 
Appot89 said:
L(n)= View attachment 20365
1) Calculate L(0): I got 2/3
2) Calculate L(1) using integration by parts: I got 4/15
3) Show that for every natural number n of (2n+3)*L(n)=2*n*L(n-1). Please help me on solving this problem. I tried using integration by parts but could not ptove this statement..
Click to expand...
I agree with you on the first two parts. It may help if you show your work for part 2, as it is similar to what you have to do for part 3, but it will not necessarily lead you directly to the best way. What we need to see is your work on part 3, so we can either find a specific error, or suggest a different way to split into parts. You may be closer than you think!
 
It's good, you're almost there! Distribute into the (1-x). The -x part will give you a L(n) term that you can combine to the left hand side.
 
When, and how, did that work get added to the OP? That should have been a response to what we'd written, so we'd be notified of it.

But, yes, that's most of the work. Just distribute and stare at what you get.
 
Dr.Peterson said:
When, and how, did that work get added to the OP? That should have been a response to what we'd written, so we'd be notified of it.

But, yes, that's most of the work. Just distribute and stare at what you get.
Click to expand...
That was my fault - again. I added that from his attempt to correct his response. But I did add there at the bottom as [added later].
 
A
Dr.Peterson said:
When, and how, did that work get added to the OP? That should have been a response to what we'd written, so we'd be notified of it.

But, yes, that's most of the work. Just distribute and stare at what you get.
Click to expand...
Alright, Thanks a lot! That was very helpful
 
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