Sum of 1/i

Find the sum of
where i=\sqrt{\textrm{-}1}.
Source: NCTM Mathematics Teacher, February 2006

Multiply both sides by 1/i

The above expression has 27 terms with the middle term equal 27
We combine the first term to the last term, the second to the next to last and so on
We end up with seven -54 terms, six +54 terms and the middle term 27. The six -54 terms cancel the six +54 terms leaving the remaining two terms -54+27=-27.

Answer: -27i
Alternative solution
We combine the terms in pairs
We end up with thirteen \textrm{+}2 terms and the remaining term -53


About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s