Thread: finding the values of constant c.....

1. finding the values of constant c.....

For what values of the constant c do the following define mas functions on the positive integers: x = 1,2,...?

f(x) = c2^(-x) / x

can someone point me the right direction? I don't know where to get started

thanks

2. $\displaystyle \sum\limits_{k = 1}^\infty {\frac{1} {{k \cdot 2^{^k } }}} = ?$

3. So you know the sum of the probability mass function has to equal one. This is the definition of a pmf. So set up the sum as Plato pointed out, set it equal to one, and solve for c.

4. i did some easier pmf problems in my text, where x goes from 1 to 4 and that's easy to solve for c.

but for this problem....

1/2c + 1/8c +1/24c +....... = 1
but what value is it when it goes to infinity?

5. Originally Posted by ixi
i did some easier pmf problems in my text, where x goes from 1 to 4 and that's easy to solve for c.
but for this problem.... 1/2c + 1/8c +1/24c +....... = 1
but what value is it when it goes to infinity?
Did you see my first post?
$\displaystyle \sum\limits_{k = 1}^\infty {\frac{1}{{k \cdot 2^{^k } }}} = \ln (2)$

6. but where did the ln(2) come from?

7. Originally Posted by ixi
but where did the ln(2) come from?
For folks working these sorts of problems that is a well known sum.

8. Originally Posted by Plato
For folks working these sorts of problems that is a well known sum.
Oh i see.

There are 2 other parts to this question that are similar. Is there a table or site you could direct me to that would have these sums?