Write the series using sigma notation

What have you tried? How far have you gotten? Where are you stuck?

Please be specific.

Thank you.

Eliz.
 
I notice that when i subtract one term from the next, I get this
2+5+10+17+26+27
3 5 7 9 11
2 2 2 2
This is where i am stuck
I dont know how I should i write it in the notation
thanks
 
Hello, bryan-duong!

I notice that when i subtract one term from the next, I get this:
\(\displaystyle \;\;2\;\;\;5\;\;\;10\;\;17\;\;26\;\;37\)
\(\displaystyle \;\;\;\;3\;\;\;5\;\;\;7\;\;\;9\;\;11\)
\(\displaystyle \;\;\;\;\;\;2\;\;\;2\;\:\;2\;\;\:2\)
Click to expand...
Since the second differences are constant, the function is a quadratic (second degree).

You can "eyeball it . . . note that every term is one more than a square:
\(\displaystyle \;\;1^2\,+\,1,\;2^2\,+\,1\,\;3^2\,+\,1,\;4^2\,+\,1,\;5^2\,+\,1,\;6^2\,+\,1\)

The general term is: \(\displaystyle \,n^2\,+\,1\)

In sigma notation: \(\displaystyle \L\,\sum^6_{n=1}(n^2\,+\,1)\)
 
You must log in or register to reply here.
Top