MATHEMATICS COLLEGE

Use induction to prove the following formula is true for all integers n where n greaterthanorequalto 1. 1 + 4 + 9 + .. + n^2 = n(n + 1)(2n + 1)/6

Answers

Answer 1
Answer:

Answer with Step-by-step explanation:

Since we have given that

1+4+9+........................+n² = (n(n+1)(2n+1))/(6)

We will show it using induction on n:

Let n = 1

L.H.S. :1 = R.H.S. : (1* 2* 3)/(6)=(6)/(6)=1

So, P(n) is true for n = 1

Now, we suppose that P(n) is true for n = k.

1+4+9+...................+k^2=(k(k+1)(2k+1))/(6)

Now, we will show that P(n) is true for n = k+1.

So, it L.H.S. becomes,

1+4+9+......................+(k+1)^2

and R.H.S. becomes,

((k+1)(k+2)(2k+3))/(6)

Consider, L.H.S.,

1+4+9+..+k^2+(k+1)^2\n\n=(k(k+1)(2k+1))/(6)+(k+1)^2\n\n=k+1[(k(2k+1))/(6)+(k+1)]\n\n=(k+1)[(2k^2+k+6k+6)/(6)]\n\n=(k+1)(2k^2+7k+6)/(6)]\n\n=(k+1)(2k^2+4k+3k+6)/(6)]\n\n=(k+1)[(2k(k+2)+3(k+2))/(6)]\n\n=((k+1)(2k+3)(k+2))/(6)

So, L.H.S. = R.H.S.

Hence, P(n) is true for all integers n.

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The directions for a calculation problem are to subtract 7 from 16 and then multiply by 4. Which expression shows this calcu

Answers

Answer:

(16-7)x4

Step-by-step explanation:

You put 16-7 in parenthesis so it means to do it first, then multiply by 4.

What is the surface area of the pyramid 8in 8 in 6in.

Answers

Answer:

mhbdjhdfvvbjd

Step-by-step explanation:

hbgjtrhkbgb

Answer:

384 inches

Step-by-step explanation:

A=lwh

Harva ate 5/8 of a medium pizza .elizabeth ate 1/4 of the pizza.how much pizza did they eat together?please show your work

Answers

Elizabeth technically ate 2/8ths of the pizza, combined with Harva's 5/8, so together they ate 7/8ths of the pizza

What is the difference? StartFraction x Over x squared + 3 x + 2 EndFraction minus StartFraction 1 Over (x + 2) (x + 1) EndFraction
StartFraction x minus 1 Over 6 x + 4 EndFraction
StartFraction negative 1 Over 4 x + 2 EndFraction
StartFraction 1 Over x + 2 EndFraction
StartFraction x minus 1 Over x squared + 3 x + 2 EndFraction

Answers

Answer:

The answer is option D.

Step-by-step explanation:

First we must first find the LCM

The LCM of x² + 3x + 2 and (x + 2)(x + 1 ) is

x² + 3x + 2

So we have

\frac{x}{ {x}^(2) + 3x + 2 } - (1)/((x + 2)(x + 1)) \n \n = \frac{x - 1}{ {x}^(2) + 3x + 2 }

Hope this helps you

Answer:

The answer is OPTION D!

Step-by-step explanation:

HoPe ThIs HeLpS!

I will mark as brainliest!!!Rewrite as a simplified fraction.
0.67 = ?
7 is repeating

Answers

Answer:

61/90

Step-by-step explanation:

What is the measure
of angle x?

Answers

Answer:

A.) 48°

Step-by-step explanation:

There is a right angle and an angle of 42°

Therefore

x=180-90-42. (sum of int angles of triangle)

x=48°

Answer:

(A) 48

Step-by-step explanation:

Triangles have 180°, so all you have to do is subtract the numbers you already know from 180.

180-42 = 138

The square on the left corner means that degree is a right angle. Right angles are always 90°.

138-90 = 48degrees

If I helped at all please give brainliest! :)
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