Closed forms of summations and reprospective relations

Hello and have a nice week !

Im asking your help with the following exercices (tried but failed).

So the first one

Find the closed form of the double summation

S(from j=1 to n) S(from i=0 to infinity) j^5/3 (1-1/2j^1/3)^I

The second one

(a) T(n)=T(n/4)+log4_n and T(1)=0 fond the closed form .

(b) A flower can live for 2 years and reproduct once a year.Specifically it reproducts during its first year of life . Find a reprospective relation that describes the number of flowers in time n and then find a closed form if we know that in time 0 there is only one flower.

Thanks in advance !!!!

Re: Closed forms of summations and reprospective relations

Quote:

Originally Posted by

**grainofsand**

So the first one

Find the closed form of the double summation

S(from j=1 to n) S(from i=0 to infinity) j^5/3 (1-1/2j^1/3)^I

Put in sufficient brackets to make your expressions unambiguous!, As it stands there is no closed form as the inner sum is divergent.

So let us assume you mean:

Write it as:

Now the inner sum is an infinite geometric series with sum:

...

CB

Re: Closed forms of summations and reprospective relations

Quote:

Originally Posted by

**CaptainBlack** Put in sufficient brackets to make your expressions unambiguous!, As it stands there is no closed form as the inner sum is divergent.

So let us assume you mean:

Write it as:

Now the inner sum is an infinite geometric series with sum:

...

CB

really thanks for the help !(Rofl)(Rofl)(Rofl)(Rofl)(Rofl)(Rofl)

i solved the first one !!!!!!!

But what about the other one with the 2 parts ????

And again thanks in advance !

for the second one part a i found sth but i dont think it is right (cause i dont even use the t(1)=0).

T(n)=O((log4_n)*n^(log4_2) How can i find the closed form of the reprospective relation ?

and what about the part b ?