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High School Archive

Browse High School Sequences, Series
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Selected answers to common questions:
    Strategies for finding sequences.

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Tricky Infinite Series and Radius of Convergence [04/21/2008]

We've found a radius of convergence for the sum of the infinite series (4/3)^n * [n!(1*4*7*10...{3n-2})] / [(2n)!], but have not been able to analyze the right endpoint of that radius. Can you help?

Trigonometric Equation for a Sequence [04/03/2001]

I need an equation for the sequence 0, 0, 1, 0, 0, 1, 0, 0, 1, ... using the sine or cosine function.

Two Arithmetic Series [7/1/1996]

an and bn are two arithmetic series; An and Bn are sums of first n elements. If (4n+27) * An = (7n+1) * Bn, compute a11/b11.

Two Ways to Find a Formula [04/14/1998]

I need to show that Sigma(rx^r) = (x-(n+1)x^(n+1)+nx^(n+2))/(1-x)^2.

Unique Subset of Set of Fractions [7/19/1996]

How can I determine a set of fractions such that if I add any subset of those fractions, I get a result that is unique relative to the result of any other subset in this set?

Using Sine and Tangent to Find Pi [08/01/1998]

How can I determine the sine or tangent of an angle without using a calculator?

Using the Comparison Test to Determine if a Series Converges [05/19/2005]

A discussion of how to apply the Comparison Test in general and in specific to the series sum n = 3 to infinity of 1/[[ln(n)]^ln(n)].

Using the Geometric Mean in a Sequence [07/11/2000]

How do you use the geometric mean to find the missing number in the geometric sequence 5,15,_,135,405?

Volume of Water in an Urn [11/12/1996]

An urn contains 1 liter of water; a second urn nearby is empty. After pouring the water back and forth 1,200,000 times in a certain way, how much water is left in each urn?

What are Taylor series? [04/18/1999]

What are Taylor Series? What are they needed for?

What Comes Ninth? [11/07/2010]

A student wants to know the next number in a sequence of integers. Doctor Ali reveals a pattern.

What is a continued fraction? [03/06/1998]

What is a continued fraction and what makes it different from the types of fractions or ratios I'm used to?

What is Meant by "the Sum of a Series"? [10/21/2003]

A series is the sum of consecutive terms. So why do many authors speak about "the sum of a series" if the name "series" already means "sum of consecutive terms"?

What is the nth Term? [08/02/1997]

The first four terms of a sequence are 16, 8, 4, 2. Find the next two terms and the rule for the nth term.

Which Elements are Divisible by 11? [07/12/1999]

Determine all solutions w = x+y+z, (1/w) = (1/x)+(1/y)+(1/z). In a given sequence, find which elements of the sequence are divisible by 11.

Why is a Telescoping Series Called Telescoping? [03/29/2008]

I understand what a telescoping series is, but I'm curious why it is referred to as 'telescoping'. What's the reason for that name?

Why Study Sequences and Series? [02/26/1999]

What are some applications of arithmetic sequences and series?

Why Use Radians instead of Degrees? [09/25/2001]

Consider Maclaurin's theorem, from which we derive the Taylor series...

Working with Sequences [11/14/1998]

Give the next two terms of the sequence: 1, 1, 2, 4, 3, 9, ....

Writing Sigma Notation [02/03/1999]

What does the equation that goes under the Sigma notation imply?

Wrong Number in a Sequence [08/13/1999]

In the sequence {1, 1, 2, 2, 6, 18, 21, 84, 88, ...} which number is incorrect? What number does it need to be replaced with?

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