3 years ago

Prove that (2n+1)^2 - (2n+1)^2 is a multiple of 8 for all positive integer values of n

Mathematics

1 answer:

kogti [31]3 years ago

4 0

Answer:

(2n + 1)[(2n + 1) � 1]

(2n + 1)(2n + 1 � 1)

(2n + 1)(2n), or 2n(2n + 1)

2n is an EVEN NUMBER, and adding 1 to an even number creates an ODD number

Therefore, 2n(2n+1)=EVEN NUMBER ODD NUMBER=EVEN NUMBER

Step-by-step explanation:

You might be interested in

Let f be the function given by the sum of the first three nonzero terms of this series. The maximum value of |lnx-f(x)| for .3&l

kodGreya [7K]

Answer:

Step-by-step explanation:

f(x) = sin(4x)f' = 4 cos(4x)f'' = -16 sin(4x)f''' = -64 cos(4x)f⁽⁴⁾ = 256 sin(4x)f⁽⁵⁾ = 1024 cos(4x)The 4-th order Taylor series expansion isf(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4!)f⁽⁴⁾(x) + ...The Maclaurin series is obtained by setting x = 0.Note that sin(0) = 0 and cos(0) = 1.The non zero terms aref(h) = 4h - (4h)³/3! + (4h)⁵/5! - (4h)⁷/7! + ...Answer: f(x) =4x- 4/3+4x/5+4x7

HOPE THIS HELPED ;3 please mark Brainliest

4 0

3 years ago

Which equation represents a proportional relationship between x and y?

steposvetlana [31]

I didn’t learn this so I guess it’s C

8 0

3 years ago

1 1/4 q/9 1/16 1/25 what is the next sequence

Vera_Pavlovna [14]

Answer:

1 1/34

Good Luck ^-^

CMIIW

8 0

3 years ago

Rachel bought a sweater at the sale price of $38. The original cost of the

Rzqust [24]

Answer. C: 26.9% dicount

4 0

3 years ago

Which equation represents the line that passes through (-6, 7) and (-3, 6)?

Vaselesa [24]

Answer:

y=-3x+5

Step-by-step explanation:

y²-y¹=gradient

x²-x¹

6-7=gradient

-3+6

-1/3=gradient

y-6/x+3=-1/3

y-6=-1/3(x+3)

y-6=-1/3x-1

y=-1/3x+5

5 0

3 years ago