I don’t know the answer but I noticed you name and saw it. Nice name from shiba.
a. Recall that

For
, we have

By integrating both sides, we get

If
, then

so that

We can shift the index to simplify the sum slightly.

b. The power series for
can be obtained simply by multiplying both sides of the series above by
.

c. We have


Answer:
What question are we supposed to answer
Step-by-step explanation:
Sorry I read the whole thing multiple times and couldn’t find what the question was
If you wanted the points to be graphed use Desmo calculator they graph the points for you:)
The total number of keys equals:
12 + 5 + 11 + 2 = 30 keys
The probability to pick a sliver key is:
12/30 = 2/5
The probability to pick a copper key is:
11/30
Hope that helps