Forming a general summation of terms

[MathewsMD]

Hi,

I was trying to form a summation for ##y_1## and have provided a solution but do not quite understand how it was formulated. I was trying to look for general patters and besides a ##(-1)^{n+1}x^2n## in the numerator, I'm a little lost on how to find a general term for the denominator. Also, is the pi just another summation symbol inside of the sigma summation? Does the symbol have any other meaning? Any help regarding how to approach this questions would be greatly appreciated!

 

[Stephen Tashi]

The [itex] \prod [/itex] symbol denotes a product instead of a sum.
For example
[itex] \prod_{k=1}^3 (2k+ 1) = (2+1)(4+1)(6+1) [/itex]

 

[MathewsMD]

The [itex] \prod [/itex] symbol denotes a product instead of a sum.
For example
[itex] \prod_{k=1}^3 (2k+ 1) = (2+1)(4+1)(6+1) [/itex]

Thank you. Just wondering, how was the summation formulated, though? I can check it and it works, but would not have devised that easily myself. Any hints on catching on to this particular pattern?

 

[Stephen Tashi]

Were y1 and y2 just given to you? I notice they are handwritten. Did you derive them yourself?

 

[blue_raver22]

Hello,

It seems like you are trying to find a general term for the summation of ##y_1##. When approaching a problem like this, one strategy is to look for patterns in the terms and try to express them in a general form. In this case, you have already identified the pattern in the numerator as ##(-1)^{n+1}x^{2n}##, which is a good start.

To find a general term for the denominator, you can also look for patterns in the terms. For example, you may notice that the denominator is a summation itself, with ##2^{k+1}## as the first term and ##k## as the last term. This suggests that the general term for the denominator could be ##2^{k+1}##. However, it is important to note that without knowing the specific values for ##n## and ##k##, it is difficult to provide a precise general term.

As for the pi symbol, it is commonly used to represent the product of a sequence of terms. In this case, it may be used to indicate that the values of ##k## are being multiplied together. However, without more context, it is difficult to determine its exact meaning.

I hope this helps in your understanding of how to approach this problem. Keep looking for patterns and making connections between the terms to find a general solution. Good luck!