All categories

2 years ago

What is the sum of the sequence 1+3+5+7+...+99 Use Gauss's approach to find the following sum.

1 answer:

5 0

Gauss's approach is to add the same sequence in reverse order, namely

S=1+3+5+7+......+95+97+99
S=99+97+95+......+7+5+3+1
---------------------------------------
2S=(1+99)+(3+97)+(5+95)+......(95+5)+(97+3)+(99+1)=50*100=5000
=> sum = (2S)/2 = 5000/2=2500.

You might be interested in

A report says that "the median credit card debt of American households is zero."

kotykmax [81]

Usually the median is defined by the middle number, so without any doubts I can say that due to the fact that half of population has zero effect the overall index is zero. Hope it is clear that the last ( D.The median debt is zero because more than half of credit card debts are zero.) option is the only correct answer whereas the others ones are wrong.

4 0

2 years ago

Mega Movies hosted a film premiere on Friday night. They charged $8 for adults and $5 for children. Ninety-two adults and childr

zmey [24]

Answer:

Step-by-step explanation:

a + c = 92.....c = 92 - a

8a + 5c = 688

8a + 5(92 - a) = 688

8a + 460 - 5a = 688

3a = 688 - 460

3a = 228

a= 228/3

a = 76 <==== adults

a + c = 92

76 + c = 92

c = 92 - 76

c = 16 <=== children

4 0

2 years ago

Help! Exponential Equation WITHOUT CALCULATOR

ale4655 [162]

$
1.
(2^{x} -2^{-x})^{2} = 4^{2} \\ \\2^{2x}-2*2^{x}*2^{-x} + 2^{-2x} =4^{2} \\ \\2^{2x}-2*2^{x-x} + 2^{-2x} =4^{2} \\ \\ 2^{2x}+ 2^{-2x} - 2=16 \\ \\ 2^{2x}+ 2^{-2x} = 18

\\ \\ 2.( 2^{x})^{3} - (2^{-x}^) ^{3}= (2^{x} -2^{-x})(2^{2x}+2^{x}*2^{-x}+2^{-2x})
\\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})(2^{2x}+2^{-2x}+2^{x}*2^{-x})
\\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})(2^{2x}+2^{-2x}+1)
\\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})((2^{2x}+2^{-2x})+1)
$

$\\ \\ ( 2^{x})^{3} - (2^{-x})^{3} =(4)((18)+1)= 76
\\ \\ 2^{3x}-2^{-3x} =76
$

4 0

3 years ago

Twice a number divided by 5 gives 4<br><br>simple equations<br><br>

melomori [17]

Answer:

x=10

Step-by-step explanation:

Let the number = x

∴ 2x/5=4

∴2x=5*4

∴2x=20

∴x=20/2

∴x=10

Hope it helps you!

Mark as brainliest if you like it

3 0

3 years ago

Read 2 more answers

HELP ME pleaseeeee ill mark you as brainiest if I get two answers

sergiy2304 [10]

Question 9

Given the segment XY with the endpoints X and Y

Given that the ray NM is the segment bisector XY

NM divides the segment XY into two equal parts

XM = MY

given

XM = 3x+1

MY = 8x-24

so substituting XM = 3x+1 and MY = 8x-24 in the equation

XM = MY

3x+1 = 8x-24

8x-3x = 1+24

5x = 25

divide both sides by 5

5x/5 = 25/5

x = 5

so the value of x = 5

As the length of the segment XY is:

Length of segment XY = XM + MY

= 3x+1 + 8x-24

= 11x - 23

substituting x = 5

= 11(5) - 23

= 55 - 23

= 32

Therefore,

The length of the segment = 32 units

Question 10)

Given the segment XY with the endpoints X and Y

Given that the line n is the segment bisector XY

The line divides the segment XY into two equal parts at M

XM = MY

given

XM = 5x+8

MY = 9x+12

so substituting XM = 5x+8 and MY = 9x+12 in the equation

XM = MY

5x+8 = 9x+12

9x-5x = 8-12

4x = -4

divide both sides by 4

4x/4 = -4/4

x = -1

so the value of x = -1

As the length of the segment XY is:

Length of segment XY = XM + MY

= 5x+8 + 9x+12

= 14x + 20

substituting x = 1

= 14(-1) + 20

= -14+20

= 6

Therefore,

The length of the segment XY = 6 units

8 0

2 years ago