A function f is defined by f(x) = 1 + 6x + x2 + 6x3 + x4 + ⋯ that is, its coefficients are c2n = 1 and c2n + 1 = 6 for all n ≥ 0. Find the interval of convergence of the series. Find an explicit formula for f(x).

From the odd-degree terms, take out one copy and rewrite the series as

Then if |x| < 1, we can condense this to

Since the series we invoked here converge on -1 < x < 1, so does this one.

You cannot buy it.

Step-by-step explanation:

$450 with a 20% percent discount would be $360

Add in a sales tax of 5.25%, and it amounts to $549 in total.

Since you only have $400, you cannot buy the bike.