This problem is driving me insane [Math & Python problem, EXPERTS only]

Question

I send a message to 5 people. Then, each one send the same message to 5 different people. How could I know the number of people the message has arrived to (excluding me) after doing this circle 10 times?

Firstly, I need to figure out the formula. Then, I must translate it to python. Any help please?
I don't even know how to start (and drawing a picture would take me a lot of time).

Answer 1

If 5 people send this message to 5 different people: 5*5 = 25 or 5^2

25 people send this message to 5 other people: 25 * 5 = 125 or 5^3

125 send this message to 5 people: 125 * 5 = 625 or 5^4

In sum it should be 5 + 5^2 + 5^3 + 5^4 + ... + 5^10

Answer 2

Thank you!