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Question

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mathstudent55 · Answer

Think of the first 1 as 1/1
What are the denominators?

chris215 · Answer

55?

mathstudent55 · Answer

Term 1 has denominator 1.
Term 2 has denominator 4.
Term 3 has denominator 9.
Term 4 has denominator 16.
etc.
Do you see a connection between the term number and the actual denominator?

chris215 · Answer

oh yeah

isaiah.feynman · Answer

$$1+\frac{ 3 }{ 4 }+\frac{ 5 }{ 9 }+\frac{ 7 }{ 16 }+\frac{ 9 }{ 25 }+...$$

isaiah.feynman · Answer

For clarity. LOL

chris215 · Answer

yeah thts correct

isaiah.feynman · Answer

Okay, the expression in sigma notation is $$\sum_{n=1}^{\infty} \frac{ 2n-1 }{ n^{2} }$$

isaiah.feynman · Answer

Sorry, I wrote the answer immediately. To explain, the denominators are just the squares of the integers. The numerators are odd integers, and odd integers are of the form 2n-1, where n is an integer.

chris215 · Answer

ohhh lol that makes sense thank you!

mathstudent55 · Answer

In your case, if the sum is only the first 5 terms you showed, then it should read:

$\Large \sum_{n=1}^{5} \frac{ 2n-1 }{ n^{2} }$