Please, solve this exercice:1+2+2²+2³+2⁴+....+ 2²⁰¹¹

It can be solved by using geometric progression?

Answers

Answer 1

Answer: $1+2+2^2+2^3+2^4+...+2^(2011)\n\na_1=1;\ a_2=1\cdot2=2;\ a_3=2\cdot2=2^2;\ a_4=2^2\cdot2=2^3\n\vdots\na_(2012)=2^(2010)\cdot2=2^(2011)$

$The\ sum\ of\ a\ terms\ of\ geometric\ progression:S_n=(a_1(1-r^n))/(1-r)\n\na_1=1;\ r=2\n\nsubtitute:\n\nS_(2012)=(1(1-2^(2012)))/(1-2)=(1-2^(2012))/(-1)=2^(2012)-1\n\nOnly\ that...(606\ digits,\ if\ you\ want\ how\ length\ this\ number)$

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In a sale, there is 50% off all prices. A chair costs £17.50 in the sale. How much was it before the sale?

Simplify showing all steps:
$4i( (1)/(2)i)^2(-2i)^2$

Answers

we know that i=√-1
so we do pemdas
$(1)/(2) i$ = $( √(-1) )/(2)$
exponents
$( ( √(-1) )/(2) )^(2)= (( √(-1) )^(2))/(2^(2))$ = $(-1)/(4)$
then $(-2i)^(2)$ =-2 times -2 times i times i=4 times -1=-4
now we have

$4i( (-1)/(4) )(-4)$ = $( (-4i)/(4) )(-4)$ = $( -i)(-4)$ =4i=aprox 4√-1

the answer is 4i

A shipping container is in the shape of a right rectangular prism with a length of 2 feet, a width of 14.5 feet, and a height of 14 feet. The container is completely filled with contents that weigh, on average, 0.9 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?

Answers

Answer:

1.8k AND 57k

Step-by-step explanation:

Larrt wants to buy some carpeting for his living room. The length of the room is 2 times the width and the total area of the room is 18 square meters. What is the length of the living room?

Answers

So, the width would be 3, and if you multiply that by 2 you get 6. Which the formula for Area is length x width. So the answer for the question is 6.

Two sides of a triangle measure 8 cm and 15 cm. which could be the length of the third side?

Answers

something grater than 23.

Answer:28

Step-by-step explanation:

Triangle RST is the pre-image of triangle UVW with a scale factor of 3. Find the area of triangle UVW if the area of triangle RST is 9 cm2. a.) Set up an equation on how to solve for the missing area using the Area Ratios for Similar Figures.

b.) What is the area of triangle UVW?

Answers

A. (Area of triangle UVW)/(Area of triangle RST)=3^2=9
B. Substitute Area of triangle RST=9 into the equation above.

(Area of triangle UVW)/9=9
Area of triangle UVW =9x9=81 cm^2

What is the Pythagorean theorem?

Answers

Pythagorean theorem is A^2 plus B^2= C^2 its the formula used to find the other side of a triangle. say A is 6ft and B is 8ft. and you're trying to find the Hypotenuse. well you would multiply 6*6 and 8*8 which equals 100. you then find the square root of 100. which is 10!:) hopes this helps!

Answer:

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. Wikipedia

a² + b² = c²

a = side of right triangle

b = side of right triangle

c = hypotenuse

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