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Ksenya-84 [330]
3 years ago
7

What is the difference b/w "Binomial Series" and "Binomial Theorem"? Also give formula for each.

Mathematics
1 answer:
horrorfan [7]3 years ago
8 0

Step-by-step explanation:

\huge{\underbrace{\overbrace{\mathfrak{\pink{Answer:}}}}}

The binomial theorem states that for some a,b∈R and some k ∈Z+ ,

(a+b)k=∑n=0k(kn)ak−nbn.

The binomial series allows us to use the binomial theorem for instances when k is not a positive integer. The binomial series applies to a given function f(x)=(1+x)k for any k∈R with the condition that |x|<1 . It is stated as follows:

(1+x)k=∑n=0∞(kn)xn .

Note that the binomial theorem produces a finite sum and the binomial series produces an infinite sum.

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The sum of the first four terms of an arithmetic sequence is $10$. If the fifth term is $5$, what is the sixth term?
Nookie1986 [14]

The sixth term of an arithmetic sequence is 6

<h3>How to find arithmetic sequence?</h3>

The sum of the first four terms of an arithmetic sequence is 10.

The fifth term is 5.

Therefore,

sum of term = n / 2(2a + (n - 1)d)

where

  • a = first term
  • d = common difference
  • n = number of terms

Therefore,

n = 4

10 = 4 / 2 (2a + 3d)

10 = 2(2a + 3d)

10 = 4a + 6d

4a + 6d = 10

a + 4d = 5

4a + 6d = 10

4a + 16d = 20

10d = 10

d = 1

a + 4(1) = 5

a = 1

Therefore,

6th term = a + 5d

6th term = 1 + 5(1)

6th term = 6

learn more on sequence here: brainly.com/question/24128922

#SPJ1

7 0
1 year ago
Can someone help me with this i am confused
Eva8 [605]
Plot each point on a graph , then count how many you need to go up and then over in this case it is 8 over 1 then calculate the y int so y= 8x -25
6 0
3 years ago
At a sale on winter clothing,Cody bought two pairs of gloves and four hats for $43.00. Tori bought two pairs of gloves and two h
lara31 [8.8K]
First do 43 - 30= $13 for two hats
so for one hat you do 13 divided by 2 which equals= <u>$6.50</u> for one hat

then you do 30 - 13= $17 for two pairs of gloves
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8 0
3 years ago
In Exercises 5-7, find all the exact t-values for which the given statement is true,
bearhunter [10]

Answer:  See Below

<u>Step-by-step explanation:</u>

NOTE: You need the Unit Circle to answer these (attached)

5) cos (t) = 1

Where on the Unit Circle does cos = 1?

Answer: at 0π (0°) and all rotations of 2π (360°)

In radians:     t = 0π + 2πn

In degrees:   t = 0° + 360n

******************************************************************************

6)\quad sin (t) = \dfrac{1}{2}

Where on the Unit Circle does   sin = \dfrac{1}{2}

<em>Hint: sin is only positive in Quadrants I and II</em>

\text{Answer: at}\  \dfrac{\pi}{6}\ (30^o)\ \text{and at}\ \dfrac{5\pi}{6}\ (150^o)\ \text{and all rotations of}\ 2\pi \ (360^o)

\text{In radians:}\ t = \dfrac{\pi}{6} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{6} + 2\pi n

In degrees:    t = 30° + 360n  and  150° + 360n

******************************************************************************

7)\quad tan (t) = -\sqrt3

Where on the Unit Circle does    \dfrac{sin}{cos} = \dfrac{-\sqrt3}{1}\ or\ \dfrac{\sqrt3}{-1}\quad \rightarrow \quad (1,-\sqrt3)\ or\ (-1, \sqrt3)

<em>Hint: sin and cos are only opposite signs in Quadrants II and IV</em>

\text{Answer: at}\  \dfrac{2\pi}{3}\ (120^o)\ \text{and at}\ \dfrac{5\pi}{3}\ (300^o)\ \text{and all rotations of}\ 2\pi \ (360^o)

\text{In radians:}\ t = \dfrac{2\pi}{3} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{3} + 2\pi n

In degrees:    t = 120° + 360n  and  300° + 360n

4 0
3 years ago
Tierra bought 4 3/8 yards blue ribbon and 2 1/8 yards yellow ribbon for a craft project. how much more blue ribbon than yellow r
jasenka [17]
4 3/8-2 1/8=2 1/4 is the answer
7 0
3 years ago
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