SOLUTION: Deanna received an e-mail asking her to forward it to 10 other people. Assume that no one breaks the chain and that there are no duplicate recipients. How many e-mails will have be

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Question 186780: Deanna received an e-mail asking her to forward it to 10 other people. Assume that no one breaks the chain and that there are no duplicate recipients. How many e-mails will have been sent after 8 generations, including Deanna's?
Could you do this problem? Thank you for your help.
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The problem says that the 1st generation of
e-mail senders is Deanna, who receives one
sends emails to 10 other people
So far I have:
generation# --- emails sent
--- 1 --------------1
--- 2 --------------10
So far, 11 people have gotten emails
Now each of the 10 people send 10 emails
and
So far I have:
generation# --- emails sent
--- 1 --------------1
--- 2 --------------10
--- 3 --------------100
So far 111 people have gotten emails
Now, there are 100 people who are going to send
emails to 10 other people.

So far I have:
generation# --- emails sent
--- 1 --------------1
--- 2 --------------10
--- 3 --------------100
--- 4 --------------1000
So far, 1111 people have gotten emails
If I carry this process to 8 generations, the 8th is:
generation# --- emails sent
--- 8 --------------10000000
and the total number of people who have gotten emails is
11,111,111