Monthly Archives: May 2018

Difference of Sequences

For the sequence , what is the difference between the mean of the sequence’s first terms and the mean of its first terms? Source: NCTM Mathematics Teacher February 2008 Solution If we add the first terms by pairs we end … Continue reading

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Sums of Reciprocals

The sum of the positive divisors of is . Find the sum of the reciprocals of the positive divisors of . Source: NCTM Mathematics Teacher, February 2008 Solution Given that , the number of divisors is . The first twelve … Continue reading

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Divisible by Units Digit

The number is divisible by its units digit . How many whole numbers less than are divisible by their respective units digit? Source: NCTM Mathematics Teacher, February 2008 Solution Nine numbers: divisible by themselves Six numbers: divisible by Six numbers: … Continue reading

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Sum of 7’s

In the sum of the expression , what digit will be in the tens place? Source: NCTM Mathematics Teacher, February 2008 Solution We are adding nineteen numbers from the smallest to the largest . Note that there are nineteen in … Continue reading

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