A request for the sum of coefficients, the numbers multiplying powers of , suggests a quick input: at , every power of becomes . Evaluate the given expression there in Desmos, then remove any constant term not included in the requested sum. Don't stop at the evaluation if the target leaves out that constant.
Hints
- Hint 1
Equivalent expressions have the same value at every input. What happens to both and when you choose ? Use that input to turn the requested coefficients into a sum.
- Hint 2
At , the given form becomes , not . Evaluate the original expression at that input, then remove the constant that isn't part of the requested sum.
Step-by-step
Evaluate at 1 to find the coefficient sum
Step 1Choose an input that brings the coefficients together
The two forms are equivalent, so they have the same value for every . Call the original expression . Use in the form with and , because :
Simplify:
- Step 2
Evaluate the original expression
Type the original expression as in Desmos, then type below it. Desmos shows . So the from the first step equals .
- Step 3
Remove the constant that isn't requested
The target is , not . Subtract the given constant from both sides:
Add on a new Desmos line; it shows . So the sum of and is . Grid in 14.