# Algebra II : Sigma Notation

## Example Questions

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### Example Question #31 : Sigma Notation

Evaluate:

Explanation:

For each iteration, we will substitute  into the summation.

Expand the terms, and simplify the factorials.

Zero factorial equals to one.

### Example Question #32 : Sigma Notation

Solve:

Explanation:

For each iteration, substitute  into the expression of .  The summation symbol indicates adding the terms together.

Convert the fractions to a common denominator by multiplying all the denominators together.

Reduce the fraction.

### Example Question #33 : Sigma Notation

Solve:

Explanation:

Simplify the fractional terms inside the parentheses.

The summation starts at index seven and ends at 9.  This mean that the fraction  will be added to itself twice for each iteration.

### Example Question #34 : Sigma Notation

Evaluate:

Explanation:

In order to evaluate this summation, we will need to substitute the bottom value for the first iteration, and repeat the process for each iteration until we reach to five.

Write  and expand the terms.

Find the least common denominator and convert the fractions to the LCD.

The least common denominator is 60.

Simplify the numerators.

This value can be reduced.

### Example Question #35 : Sigma Notation

Solve:

Explanation:

This summation will start at zero and will have no more iterations after this term.

Substitute the bottom value into the expression and solve.

Any value to raised to the power of zero is equal to one.

### Example Question #36 : Sigma Notation

Evaluate:

Explanation:

Substitute  for the first iteration, and then repeat for every integer until 4 is reached.  Stop the loop after four.

Evaluate by order of operations.

### Example Question #37 : Sigma Notation

Simplify:

Explanation:

The iteration starts at zero and ends at three.

Substitute the terms and increase the value of  by one for each loop.

Simplify the terms.

### Example Question #38 : Sigma Notation

Evaluate

Explanation:

is equal to the sum of the expressions formed by substituting 1, 2, 3, and 4, in turn, for  in the expression , as follows:

The finite sequence can be restated, and evaluated, as

.

### Example Question #39 : Sigma Notation

Evaluate:

None of these

Explanation:

is equal to the sum of the expressions formed by substituting 1, 2, 3, 4, and 5, in turn, for  in the expression , as follows:

:

The finite series can be restated, and evaluated, as

.

### Example Question #40 : Sigma Notation

Evaluate:

Explanation:

Substitute the value of  for each iteration.

Simplify each term by order of operations.

Convert all with a common denominator.