Infinity Sum: Solving Sequences with Sin n(pi) / 6

Thread starter teng125
Start date Jan 20, 2006
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Sequences

In summary, a sequence problem involves finding a pattern or rule within a given sequence of numbers, usually for the purpose of predicting the next number or term. To solve a sequence problem, you need to first identify the pattern or rule, which can be done by looking for repeated differences, common ratios, or other mathematical relationships between the numbers. Some common types of sequences include arithmetic, geometric, and Fibonacci sequences. To check if your answer to a sequence problem is correct, you can plug in the predicted value and see if it follows the same pattern as the other terms in the sequence. Tips for solving sequence problems include looking for patterns or relationships, starting with simple sequences, and checking your answer.

Jan 20, 2006

teng125

hiw to solve for infinity sum (n=1) [sin n(pi)] / 6 ??
pls help...thanx

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Jan 20, 2006

Hurkyl

Staff Emeritus

Science Advisor

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Do you mean how to compute that sum? Have you tried writing out its first few values and computing the first few partial sums, to try and formulate a guess?

Jan 20, 2006

teng125

all equals to zero and converges right??

Jan 20, 2006

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

If all the terms sums are zero, then yes, it will converge!

1. What is a sequence problem?

A sequence problem is a type of mathematical problem that involves finding a pattern or rule within a given sequence of numbers. It usually involves predicting the next number or term in the sequence.

2. How do I solve a sequence problem?

To solve a sequence problem, you need to first identify the pattern or rule in the given sequence. This can be done by looking for repeated differences, common ratios, or other mathematical relationships between the numbers. Once the pattern is identified, you can use it to predict the next number in the sequence.

3. What are some common types of sequences?

Some common types of sequences include arithmetic sequences, geometric sequences, and Fibonacci sequences. An arithmetic sequence is a sequence in which each term is obtained by adding a constant value to the previous term. A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a constant value. A Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding numbers.

4. How do I know if my answer to a sequence problem is correct?

You can check if your answer to a sequence problem is correct by plugging in the predicted value for the next term into the given sequence. If it follows the same pattern or rule as the other terms in the sequence, then your answer is likely correct. You can also double-check your answer by using the pattern or rule to calculate other terms in the sequence and see if they match the given sequence.

5. Are there any tips for solving sequence problems?

Some tips for solving sequence problems include looking for patterns or relationships between the numbers, starting with simple sequences and gradually moving on to more complex ones, and checking your answer by plugging it back into the sequence. It can also be helpful to write out the sequence and label each term with its corresponding position number to better visualize the pattern.