# sigma notations

• Nov 1st 2008, 10:20 PM
tsal15
sigma notations
Hey there people and fellow mathematicians,

I need some help with the following:

The question is as stated: "Write an expression in sigma notation as shown for suitable terms $\displaystyle n_1,n_2$ and $\displaystyle a_i$ for each of these finite and infinite summations. i.e.$\displaystyle \sum\limits_{i=n_1}^{n_2} a_i$ "

$\displaystyle S_2 = 1-3+5-...\pm(2n+1)$

Here's my solution:

$\displaystyle S_2 = \sum\limits_{n=0}^{n}(-1)^{n+2}(2n+1)$

Is this correct?

Cheers :)
• Nov 1st 2008, 10:50 PM
Chris L T521
Quote:

Originally Posted by tsal15
Hey there people and fellow mathematicians,

I need some help with the following:

The question is as stated: "Write an expression in sigma notation as shown for suitable terms $\displaystyle n_1,n_2$ and $\displaystyle a_i$ for each of these finite and infinite summations. i.e.$\displaystyle \sum\limits_{i=n_1}^{n_2} a_i$ "

$\displaystyle S_2 = 1-3+5-...\pm(2n+1)$

Here's my solution:

$\displaystyle S_2 = \sum\limits_{n=0}^{n}(-1)^{n+2}(2n+1)$

Is this correct?

Cheers :)

Yes! That's correct. However, in your notation, I would let the main variable be k, as in $\displaystyle S_2 = \sum\limits_{k=0}^{n}(-1)^{k+2}(2k+1)$

Alternatively, $\displaystyle \sum_{k=0}^{n}(-1)^k\left(2k+1\right)$ is correct as well.

--Chris