Divisibility by 11 and Related Concepts

What is the rule for determining if a number is divisible by 11?

• Calculate the alternating sum of the digits

• Add all the digits together

• Check if the number is even

• Check if the number ends in 0 or 5

What is the alternating sum of the digits in 5,214?

• 11

• 0

• 5

• 2

Is 9,859 divisible by 11?

• Yes, because it ends in 9

• No, because it is an odd number

• No, because the alternating sum is -3

• Yes, because the alternating sum is 0

What is the result of dividing 5,214 by 11?

• 11

• 0

• 521

• 474

What does the expression C + 10B + 100A represent?

• The product of the digits

• The expanded form of a three-digit number

• The alternating sum of the digits

• The sum of the digits

Why is the alternating sum used in the divisibility rule for 11?

• Because it is easier to calculate

• Because powers of 10 alternate between 1 and -1 mod 11

• Because it is a common mathematical practice

• Because it is the only method that works

What is a key concept discussed in relation to divisibility rules?

• Modular arithmetic

• Prime numbers

• Geometry

• Algebra

What is the harmonic series?

• A series that converges to a specific value

• A series that is always divisible by 11

• A series that grows to infinity

• A series that alternates between positive and negative

What happens when the harmonic series is turned into an alternating sum?

• It diverges

• It remains the same

• It becomes a multiple of 11

• It converges to a specific value

To what value does the alternating harmonic series converge?

• Zero

• Natural log of 2

• Infinity

• Natural log of 10