C) is the answer 1800/36=50
There are two possibilities
Let's work backwards.
The answer will be in the form (x+a)^2 for any real number a
Now the expansion will be x^2+2ax+a^2.
We can see just from this that 2a=5/4
a=5/8
The result binomial should be x+5/8
Resulting binomial squared expansion should be x^2+5/4x+25/64
The term we need to add will be 25/64
3/4 of a pound is half of 1.5 pounds ( 3/4 + 3/4 = 1.5)
3.60 / 2 = $1.80
it will cost $1.80 for 3/4 of a pound
I suppose you mean
Recall that
which converges everywhere. Then by substitution,
which also converges everywhere (and we can confirm this via the ratio test, for instance).
a. Differentiating the Taylor series gives
(starting at because the summand is 0 when )
b. Naturally, the differentiated series represents
To see this, recalling the series for , we know
Multiplying by gives
and from here,
c. This series also converges everywhere. By the ratio test, the series converges if
The limit is 0, so any choice of satisfies the convergence condition.