Write the series using sigma notation

[Guest]

write the series using sigma notation
2+5+10+17+26+37

 

[stapel]

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

Please be specific.

Thank you.

Eliz.

 

[Guest]

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

 

[soroban]

Hello, bryan-duong!

I notice that when i subtract one term from the next, I get this:
$\displaystyle \;\;2\;\;\;5\;\;\;10\;\;17\;\;26\;\;37$
$\displaystyle \;\;\;\;3\;\;\;5\;\;\;7\;\;\;9\;\;11$
$\displaystyle \;\;\;\;\;\;2\;\;\;2\;\:\;2\;\;\:2$

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: \(\displaystyle \L\,\sum^6_{n=1}(n^2\,+\,1)\)

 

[Guest]

Whow
thanks for yr response
it helps alot