Solve for k: Difference between nth terms of two series > 14

[oilersforever72]

Homework Statement

Hi, it's been a while since I've done questions such as the one below. Does anyone know how to solve it? (Note that k and n are actually sub-k and sub-n). Thanks in advance.

The kth term of a series, Sk = a (1-R^k) / (1-R) , is the sum of the first k terms of the underlying sequence. The difference between the nth terms of two particular series is greater than 14 for some values of n (all of which are real numbers). The series with the general term, tn = 100 (11/17)^n-1 begins larger than the second series with general term tn = 50(14/17)^n-1. Find the largest natural number, k, where the difference between the terms of these two series is larger than 14.

I don't even understand what it's asking for :S Please dumb it down as much as you can, haha.

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Homework Statement

Hi, it's been a while since I've done questions such as the one below. Does anyone know how to solve it? (Note that k and n are actually sub-k and sub-n). Thanks in advance.

The kth term of a series, Sk = a (1-R^k) / (1-R) , is the sum of the first k terms of the underlying sequence. The difference between the nth terms of two particular series is greater than 14 for some values of n (all of which are real numbers).

I'm having a bit of trouble following this. S_k is the k^th partial sum? Are you saying that the n^th terms of the [sequences are real numbers? The way you phrased it makes it sound like it is the values of n that are real- but they should be positive integers! I don't see how knowing about "some values of n" will tell you anything about the series itself.

The series with the general term, tn = 100 (11/17)^n-1 begins larger than the second series with general term tn = 50(14/17)^n-1.

Is that (100(11/17)^n)- 1 or 100(11/17)^(n-1)?

Find the largest natural number, k, where the difference between the terms of these two series is larger than 14.

I don't even understand what it's asking for :S Please dumb it down as much as you can, haha.

Might be a good idea to use different letters for these series: call t_n= 100(11/17)ⁿ- 1 and s_n= 50(14/17)ⁿ-1. Their difference is t_n- sn[/sub]= 100(11/17)ⁿ- 50(14/17)ⁿ= 2(50(11/17)ⁿ- (14/17)ⁿ. They are asking you to find the largest k such that 2(50(11/17)^k- (14/17)^k> 14 or 50(11/17)^k- (14/17)^k= 7.

Homework Equations

The Attempt at a Solution

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[oilersforever72]

sorry man... that's part of my problem... this is the question as i got it... and i have no idea what it's saying. i think even if you couldn't figure out the answer, some guidance on how you would even approach such a question would be much appreciated. perhaps u've seen a similar question (better worded perhaps, lol)... if i could see the question and how someone answered it, i think i could take it from there... but yea... i too get confused with Sn and tn and that all that shazzz...