1. ## Sequences question

Is the solution I posted wrong?

For the last part, using L'Hopital's rule on (1 - xln(2))/2^x gives me -ln(2)/[ln(2) * 2^x] = -1/2^x = 0 (ignoring the limit operators - is operator the right word?).

Is the solution wrong or am I not seeing something?

Any input would be appreciated!

2. ## Re: Sequences question

Originally Posted by s3a
Is the solution I posted wrong?

Using L'Hopital's rule on (1 - xln(2))/2^x gives me -ln(2)/[ln(2) * 2^x] = -1/2^x = 0 (ignoring the limit operators - is operator the right word?).

Is the solution wrong or am I not seeing something?

Any input would be appreciated!

We are not megicians... WHAT is the question?!

3. ## Re: Sequences question

The question is included with the solution.

4. ## Re: Sequences question

Originally Posted by s3a
For the last part, using L'Hopital's rule on (1 - xln(2))/2^x gives me -ln(2)/[ln(2) * 2^x] = -1/2^x = 0 (ignoring the limit operators - is operator the right word?).
You have to compute $\displaystyle \lim_{x\to +\infty}\dfrac{x}{2^x}$ , an differentiate independently numerator and denominator.

Out of curiosity, I don't understand why the problem uses the function $\displaystyle f(x)$ , it is not necessary. For example for (a) $\displaystyle s_{n+1}-s_n=\ldots=\dfrac{29}{(7n+10)(7n+3)}\geq 0$ for all $\displaystyle n$ which implies $\displaystyle s_n$ is increasing and its limit is easily obtained by elemental computations. For (b) , $\displaystyle \dfrac{s_{n+1}}{s_n}=\ldots=\dfrac{n+1}{2n}\leq 1$ which implies $\displaystyle s_n$ is decreasing etc.