1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
daser333 [38]
3 years ago
7

Use mathematical induction to prove that the statement is true for every positive integer n.

Mathematics
1 answer:
Mice21 [21]3 years ago
7 0

Induction on n

Base case: n = 0

the left side is 0, and the right side is 0, so the equality holds.

Now, suppose that is true for n, and you need to show that the equality holds for n+1

So, write the left side

8 + 16 +24 + ... + 8n + 8(n+1) (*)

By hypothesis, 8+16+24+ ...+ 8n = 4n(n+1)

so, in (*) we have

4n(n+1) +8(n+1) = (4n+8)(n+1) = 4(n+2)(n+1) = 4(n+1)(n+2). So, this is true for every natural number n.


You might be interested in
How find the c intercept
zhuklara [117]

Answer:

I think you have not written down the full question

Just write it down then I might help

7 0
3 years ago
Please help!!!!!!!!!!!!!!!!!!
S_A_V [24]

Answer:

It should be the first one.


Step-by-step explanation:


8 0
3 years ago
Read 2 more answers
Which expression is equivalent to 3/2•3/2•3/2•3/2?
serg [7]

The answer is A) 2/3 ^ 4 power

5 0
3 years ago
Which is greater than, -9/4 or -3?
Firdavs [7]

-9/4 is greater than -3 because -9/4 is also -2.25 and the less negative number is always greater than the more negative number.

Hope this helps!


7 0
3 years ago
Read 2 more answers
How do I simplify this (sinx)/(secx+1)
pochemuha

Answer:

Step-by-step explanation:

\frac{sin~x}{sec~x+1} =\frac{sin~x}{\frac{1}{cos~x}+1  } =\frac{sin~x~cos~x}{1+cos~x} \\=\frac{sin~x~cos~x}{1+cos~x} \times \frac{1-cos~x}{1-cos~x} \\=\frac{sin~x~cos~x(1-cos~x)}{1-cos^2 x} \\=\frac{sin~x~cos~x(1-cos~x)}{sin^2x} \\=\frac{cos~x(1-cos~x)}{sin~x} \\=cos ~x(csc~x-cot~x)\\or\\=cot~x(1-cos~x)

6 0
3 years ago
Other questions:
  • How long is the arc subtended by an angle of 9π/5 radians on a circle of radius 30 cm?
    13·1 answer
  • In the 1939 movie The Wizard of Oz, when the brainless Scarecrow is given the confidence to think by the Wizard(by merely handin
    11·1 answer
  • A football field has the shape of a rectangle with dimensions of 300 feet long and 160 feet wide. If a fan was to run diagonally
    12·2 answers
  • What is 75/100 simplified
    13·2 answers
  • Explain why you usually need to use to find the volume of a cylinder.
    6·2 answers
  • Solve 14n &gt; 11n + 6<br><br> please help
    12·2 answers
  • Solve: 4(7x-11) +4 = 96 M Insert picture of work​
    10·1 answer
  • Is anyone good at geometry if so can someone help me please ?
    8·1 answer
  • The initial amount of money that is deposited into an account or that is borrowed is called what
    6·2 answers
  • Help me pwesssssssssss
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!