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.
Answer: The answer is (b) (2, ∞)
Step-by-step explanation: We are given a function f(x) in the figure and we are to select out of the given options that accurately shows the range of the function defined.
Therefore, the range of the function f(x) will be greater then or equal to 2. So, the range will be [2, ∞).
Thus, the correct option is (b) (2, ∞).
The given sum for n = 1 to n = 15 is equal to 255, so the correct option is B.
<h3>
How to find the sum of the given series?</h3>
We want to find the sum of the series whose elements are of the form:
(2n + 1)
From n = 1 to n = 15.
Then our sum will be:
(2*1 + 1) + (2*2 + 1) + ... + (2*15 + 1).
3 + 5 + ... + 31
This is the sum of all odd numbers in the interval [3, 31]
Which gives:
So the correct option is B.
If you want to learn more about sums:
brainly.com/question/24295771
#SPJ1
Answer:
To solve fractions, you MUST HAVE THE SAME DENOMINATORS WHEN DEALING WITH ADDITION AND SUBTRACTION.
Step-by-step explanation:
For example, 2/3 + 3/6
The denominators in this case have a common denominator which is 6.
All you have to do is multiply the 2/3 by 2 in the numerator and the denominator. Once you do, you'll get 4/6 which you could then add to 3/6 to get 7/6 which would equal 1 1/6 or 7/6 either is fine.
Hope this helps! :)
