Alan

I guess you are looking for something like the following:

1. I_total = I₁ = I₂ 

2. I_total = I₁ + I₂

3. R_total = R₁ + R₂

4. 1/R_total = 1/R₁ + 1/R₂

The number 663_b is   6b² + 6b + 3  or  3(2b² + 2b + 1)  which is the product of two integers (assuming b is an integer), hence cannot be prime for any base b.

Base 2 can only have digits 0 and 1.  No base up to and including 6 can have the digit 6 - that's why Guest #1 started at base 7.

As follows:

This question was asked and answered here: https://web2.0calc.com/questions/help_84836#r5

Here's a systematic way of approaching this:

"lim" is short for limit.  It means take the limit, so, for example  \(\lim_{x\rightarrow 0}(x^2-3)\) means take the limit of the expression x² - 3 as x goes to zero.

The "weird E thing" is the summation sign (it's the Greek upper case letter sigma), so for example \(\sum_{k=1}^3x_k\) is the same thing as x₁ + x₂ + x₃.

Perhaps the following will make it clearer:

EP made the trivial mistake of setting 1 hour 45 mins (i.e. one and three quarter hours) as 1.45 hours rather than 1.75 hours

Now see how you get on with your question 4) . 

Ok!!!

Multiply S by 2³ so 8S = (2/2)³ + (2/4)³ + (2/6)³ + ... = 1/1³ + 1/2³ + 1/3³ + ... = S + T

So:  8S = S + T

Divide both sides by T and rearrange. I’ll leave you to do this.