Help with difference equation (hard undergrad calculus)

Suppose that the sequence pi1, pi2, pi3,....... Satisfies the recurrence relation

Pi(sub n+1) * n/(n+1) = Pi(sub n)/n for n=1,2,3,....

Along with the condition sumof(Pi(sub n)) = 1 from n>=1.

What is the value of Pi(sub 1)?

Sub = subscript

Now I don't know where to start.

Thanks for help!

please post a photo of the question

Lol
Sub=subscript
Wtf does that mean.


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please post a photo of the question

Managed to upload it.

Managed to upload it.

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I just looked at it over dinner and I got it as 1/(2e-1)
which is not there (clearly I am making an error somewhere)

I am desperate to get this right as I want it for my own library of resources

I just looked at it over dinner and I got it as 1/(2e-1)
which is not there (clearly I am making an error somewhere)

I am desperate to get this right as I want it for my own library of resources

I have some more super tricky questions coming up!

I think it's 0.5e^-1

I think it's 0.5e^-1

I have some more super tricky questions coming up!

this is my solution... I cannot get any of the 4 answers there, but someone can check where I have gone wrong.
I hope I have not made any embarrassing error for which I am notorious

Your infinite sum starts at $P_2$ (i.e. you are finding $\sum_2^\infty P_k$ when it should be $\sum_1^\infty P_k$).

this is my solution... I cannot get any of the 4 answers there, but someone can check where I have gone wrong.
I hope I have not made any embarrassing error for which I am notorious

Gome44 is correct. The answer is 0.5e^-1

see the method I posted
there is a tiny error in the adding (see if you can spot it)
then there is your question ...

haha thanks!

some tough question to understand