Investigating Infinite Summation: Calculating Sn 0-10

[Peter G.]

I am investigating the sum of infinite sequences.

such that: t₀ = 1 and t_n = (x ln (a))ⁿ/n!

They tell me to first consider the following sequences of terms:

1, (ln 2)/1, (ln 2)²/2x1, (ln 2)³/3x2x1

They then ask me to calculate the sum S_n of the first n terms of the sequence for when 0 is bigger or equal to 0 and smaller or equal to 10.

I couldn't however, find any relationship between the terms that indicates whether the sequence is arithmetic or geometric.

So are they asking me to simply grab the calculator, calculate the values and write them down?

Thanks,
Peter G.

 

[HallsofIvy]

I am investigating the sum of infinite sequences.

such that: t₀ = 1 and t_n = (x ln (a))ⁿ/n!

They tell me to first consider the following sequences of terms:

1, (ln 2)/1, (ln 2)²/2x1, (ln 2)³/3x2x1

Please, please, please don't us "x" both as a variable and as a multiplication symbol!
I think you mean 1, (ln 2)/1, (ln 2)²/(2)(1)m, ln(2)³/3(2)(1), etc.

They then ask me to calculate the sum S_n of the first n terms of the sequence for when 0 is bigger or equal to 0 and smaller or equal to 10.

"0 is bigger or equal to 0" surely that's not what you meant!

I couldn't however, find any relationship between the terms that indicates whether the sequence is arithmetic or geometric.

There is a reason for that! The quotient ((ln 2)/1)/1= ln(2) while ((ln(2))²/2)/(ln(2)/1)= ln(2)/2. Since those are not equal, this is NOT a geometric sequence. The difference ln(2)/1- 1 is not equal to ((ln(2))²/6)/((ln(2))/1) so this is NOT a an arithmetic sequence.

So are they asking me to simply grab the calculator, calculate the values and write them down?

Yes, although I have still not figured out what you really meant by "calculate the sum S_n of the first n terms of the sequence for when 0 is bigger or equal to 0 and smaller or equal to 10". Is it possible that you are to calculate this for n between 0 and 10?

Thanks,
Peter G.

 

[Peter G.]

I am very sorry. Reading over what I wrote is actually quite embarrassing. I actually moved this post to the Calculus region because I saw a post with the exact same problem as mine there.

I made some progress with the people in that section, but, in case I have future doubts and you want to contribute, you can find the topic at:

https://www.physicsforums.com/showthread.php?p=3276495&posted=1#post3276495

Sorry once again,
Peter G.