Infinite Series and Sigma Notation

The video tutorial explains how to define a sub n for an infinite series starting from n equals 2 to infinity. It identifies patterns in the numerators and denominators of the series terms, showing that the numerators are powers of negative 2 and the denominators follow a specific pattern. The tutorial concludes by expressing the series in sigma notation.

What is the starting index of the infinite series discussed in the video?

• 2

• 3

• 1

• 4

What is the value of a sub 2 in the series?

• 16/7

• -8/5

• -32/9

• 8/5

How is the pattern in the numerators of the series described?

• Subtracting 4

• Multiplying by -2

• Adding 5

• Multiplying by 3

What power of negative 2 is equal to 16 in the series?

• Negative 2 to the second power

• Negative 2 to the third power

• Negative 2 to the fifth power

• Negative 2 to the fourth power

What is the relationship between the index and the exponent in the numerators?

• Exponent is two less than the index

• Exponent is three more than the index

• Exponent is equal to the index

• Exponent is one more than the index

What is the denominator when n is 3?

• 5

• 7

• 9

• 11

How do the denominators change as the index increases?

• Increase by 3

• Increase by 1

• Remain constant

• Increase by 2

What is the formula for the denominator in terms of the index?

• 2n - 1

• n + 2

• 2n + 1

• 3n + 1

How is the series expressed in sigma notation?

• Sum from n equals 2 to infinity of 2 to the n over n plus 1

• Sum from n equals 2 to infinity of negative 2 to the n plus 1 power over 2n plus 1

• Sum from n equals 1 to infinity of negative 2 to the n over 2n

• Sum from n equals 3 to infinity of negative 2 to the n over n

What is the final expression for a sub n?

• Negative 2 to the n plus 1 over 2n plus 1

• Negative 2 to the n plus 1 over 2n

• 2 to the n over n plus 1

• Negative 2 to the n over n