kayleerichards666
23.06.2021 •
Mathematics
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
(4 points each.)
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six
12 + 42 + 72 + ... + (3n - 2)2 = quantity n times quantity six n squared minus three n minus one all divided by two
For the given statement Pn, write the statements P1, Pk, and Pk+1.
(2 points)
2 + 4 + 6 + . . . + 2n = n(n+1)
Solved
Show answers
More tips
- S Style and Beauty Tricks and Tips: How to Get Rid of Freckles...
- H Health and Medicine How to perform artificial respiration?...
- C Computers and Internet How to Get Rid of Windows Genuine Check?...
- F Food and Cooking The Disease That Haunted Abraham Lincoln...
- S Style and Beauty How to Make Your Lips Fuller? Ideas and Tips for Beautiful Lips...
- S Style and Beauty How are artificial nails removed?...
- F Family and Home How to Sew Curtain Tapes: Best Tips from Professionals...
- H Horoscopes, Magic, Divination How to Cast a Love Spell on a Guy? Guide for Guys...
- F Family and Home How to Properly Use a Water Level?...
- L Legal consultation What Documents Are Required for a Russian Passport?...
Answers on questions: Mathematics
- M Mathematics 59, 51, 55, 46, 50, 40, 44, ,...
- M Mathematics What is the ratio of 40cm and 18mm...
- M Mathematics Simplify 5^ 3log(5)^6...
- M Mathematics Who still watches this tha sho be poppin my crib off tha shid no cap my bois and girls...
- M Mathematics Solve the system using the linear combination method: X + 5y = -3 2x + 7y= 3 (-2,1) (-13,2) (22,-5) (12,-3)...
- M Mathematics Connie bought 172 tulip bulbs. She wants to plant an equal number of bulbs in each of 4 flower beds. How many bulbs should Connie plant in each flower bed? (wrong answer will...
- M Mathematics How do you determine which variable is independent and which one is independent?...
- M Mathematics What flavor of ice cream would you pick? Chocolate Vanilla Neither Children 40 Teens 12 16 45 Adults 55 54 22 15 10 The table shows the results of a survey on the preferred...
- M Mathematics The dimensions of a rectangle are shown. What is the area of the rectangle?...
- M Mathematics Selected Technologies According to recent surveys, 60% of households have personal computers. If a random sample of 150 households is selected, what is the probability that...
Ответ:
1. The given series is
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) =
For n=1
L.H.S=4.6=24
R.H.S=[4×5×15]÷6
=300÷6
=50
So, for n=1,
L.H.S≠ R.H.S
Since the given expression is true for n=1 ,
So , the given series is untrue.
we should replace R.H.S by=4(n+1)(n+2)(4n-3)²
2.
12+42+72++(3 n -2)2=
For n=1,
L.H.S=12
R.H.S=1×(6-3-1)/2
=2/2
=1
As L.H.S≠ R.H.S
We should Replace R.H.S by [(3 n-1)(3 n-2)]2
3.The given sequence is
2+4+6++2n=n(n+1)
L.H.S
P(1)=2
R.H.S
1×(1+1)
=1×2
=2
( b) L.H.S
P(n)=2+4+6+2 k
This is an A.P having n terms.
tex]S_{n}=
= n(n+ 1)
R.H.S=n(n+1)
So, P(k)=k(k+1)
(c) P(k+1)=2+4+6++2(k+1)
This is an A.P having (k+1) terms.
=(k+1)(k+2)
So, P(k+1)= (k+1)(k+2)
(Btw this is not my answer)
Ответ:
Solving this equation for circumference:
circumference = arc length / (central angle / 360)
circumference = 12 / (85/360)
circumference = 12 / 0.2361111111
circumference = 50.8235294118
Source:
http://www.1728.org/radians.htm