Finding Value of \sum_{i=1}^{n}: Intro to Integration

[mateomy]

We're going over the intro stuff to integration and we are being asked to find the value of the sums...

Here's the problem I am getting stuck on...

$$\sum_{i=1}^{n} (i^2 + 3i + 4)$$

I know that I have to separate the individual sums, so I put it into this form...

$$\sum_{i=1}^{n} i^2 + 3\sum_{i=1}^{n} i + \sum_{i=1}^{n} 4$$

And then I know the individual forms of the Riemann sums of i^2 and i, etc.

$$\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6} etc, etc...$$

am I just adding these together as if they were fractions (finding common denominators, etc)?

 

[micromass]

Yes, you could just put them together like fractions.

 

[mateomy]

Awesome, thanks.