Question

You start a chain email and send it to six friends. The next day, each of your friends forwards the email to six people. The process continues for a few days.

Answer 1

Solution:

The following information about the chain email can be Written as follows:

1 Person Email →→6 Persons (E-mail) →6² Persons  (E-mail)→6³ Persons  (E-mail)+.........few Days

As you can see the number of email sent starting from person 1 to 6 persons to 36 persons to 216 persons, forms a Geometric pattern.

So, Sum of the Series = 1 + 6 + 36 + 216 + 1296 +......+  for n days

        = $1+6^1+6^2+6^3+6^4 +6^5 +6^6+..........+ 6^n$

Formula for n terms of a geometric series

$\frac{a (r^n-1)}{r-1}$

For, Common ratio (r)≥1

Sum of above geometric series up to n terms $=\frac{6^n-1}{6-1}=\frac{6^n-1}{5}$