### Home > APCALC > Chapter 2 > Lesson 2.2.3 > Problem2-82

2-82.

Examine the expanded sums below and write the equivalent sigma notation.

1. $\frac { 2 } { 3 } f ( - 2 + \frac { 2 } { 3 } \cdot 0 ) + \frac { 2 } { 3 } f ( - 2 + \frac { 2 } { 3 } \cdot 1 ) + \frac { 2 } { 3 } f ( - 2 + \frac { 2 } { 3 } \cdot 2 ) + \frac { 2 } { 3 } f ( - 2 + \frac { 2 } { 3 } \cdot 3 )$

Are there any common terms that can be factored out?

Notice what changes and what stays the same.

The variable (or variable expression) represents what changes. The index represent what will be plugged into the variable.

$\displaystyle \sum_{k=0}^{3}\frac{2}{3}f\left( -2+\frac{2}{3}k \right )$

2. $\frac { 1 } { 2 } f ( 6 + \frac { 1 } { 2 } \cdot 0 ) + \frac { 1 } { 2 } f ( 6 + \frac { 1 } { 2 } \cdot 1 ) + \frac { 1 } { 2 } f ( 6 + \frac { 1 } { 2 } \cdot 2 ) + \frac { 1 } { 2 } f ( 6 + \frac { 1 } { 2 } \cdot 3 ) + \frac { 1 } { 2 } f ( 6 + \frac { 1 } { 2 } \cdot 4 )$

Refer to the hints in part (a).