Math Is Fun Forum

Gang Green

Guest

Compact Expressions

I'm in a class called Fixed-Income Mathematics (bond math, interest rates, etc).

One question asks to find the compact expression of the sum.

examples: (These are all in sigma notation, n=0 to N)

n^3 x^n
n(n+2)x^n

My question is, what is compact expression form?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Compact Expressions

First we calculate

.

                       

                       

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Compact Expressions

By fiddling with the formula

we get

And

Now let

Using the same trick as before, we get

                 

                 

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Compact Expressions

So the answer to your second question is

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Compact Expressions

For your first question, if you let

you get

And this time I will leave you to complete the job yourself.