Solve for m d=n+7m Thank you
2 answers:
Answer:
This is the same as writing m = (d-n)/7
The parenthesis are essential for the second format because it tells us to divide all of (d-n) over 7, and not just n over 7.
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Explanation:
Here is one way to solve for m. I'll go over each step in the next section below.
The idea is to get the variable m by itself.
Think of n+7m as 7m+n since we can add in any order. Then undo the "plus n" portion by subtracting n from both sides (step 3).
In the 4th step, I divided both sides by 7 to undo the multiplication that is going on with 7m aka 7*m
In general we follow PEMDAS backwards to undo each operation done to the variable we're solving for. Let me know if you have any questions about what I mean.
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I bet the sum you're referring to is supposed to be
or equivalently,
where is the binomial coefficient.
Recall the binomial series,
which is valid for |x| < 1. (Note that if r > α, the binomial coefficient is defined to be zero, so there really are only α many terms when α is a whole number.)
Differentiating both sides with respect to x gives
Multiply both sides by some arbitrary x in |x| < 1 :
Repeat:
Let α = 20, and let x approach 1 from below. The right side converges to the sum we want, while the left side converges to