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c) By telescoping sums, the answer is 1/3.

Could one of the moderators answer these questions if possible?

That's also incorrect, please double-check your answers before submitting.

b) The sum is 9/5.

The answer is 0 :)

It says it wrong :(

a) 

The first fraction is 3/1​.

The product of the 10 fractions is 7/2. This means that the numerator of the product is 7 and the denominator is 2. The numerator of the first fraction is 2 greater than the denominator, so the numerator is 3 and the denominator is 1.

The probability that the two cards have the same number is 10/19​.

There are 20 cards in the deck, 10 red cards numbered 1-10 and 10 blue cards numbered 1-10. The probability of drawing a red card is 10/20=1/2​. The probability of drawing a blue card is also 1/2​.

If the first card is red, the probability that the second card is also red is 9/19. If the first card is blue, the probability that the second card is also blue is 9/19​.

Therefore, the probability that the two cards have the same number is 1/2*9/19 + 1/2*9/19 = 10/19.

a=listfor(n, 0, 32 ,1 / ((1+3*n)*(1+3*(n+1)));print a, "==",sum a

(1 / 4, 1 / 28, 1 / 70, 1 / 130, 1 / 208, 1 / 304, 1 / 418, 1 / 550, 1 / 700, 1 / 868, 1 / 1054, 1 / 1258, 1 / 1480, 1 / 1720, 1 / 1978, 1 / 2254, 1 / 2548, 1 / 2860, 1 / 3190, 1 / 3538, 1 / 3904, 1 / 4288, 1 / 4690, 1 / 5110, 1 / 5548, 1 / 6004, 1 / 6478, 1 / 6970, 1 / 7480, 1 / 8008, 1 / 8554, 1 / 9118, 1 / 9700) == 33 / 100

Here's one way of approaching this:

1 + ∑[(2n + 1)/ (5^n),  n,  1,  ∞]==15 / 8 ==1.875

Hint:

Any integer is divisable by three if the its digits add up to a multiple of 3.     [sum of digits is a multiple of 2]

So what do you think the answer is?

You will have to work out 4 digit numbers, 3 digit numbers, 2 and 1 digit numbers all seperately.

sqrt2 is less than pi

so

\(h(\sqrt2)=\lfloor4\sqrt2 \rfloor \\ h(\sqrt2)=\lfloor 5.65 \rfloor \\ h(\sqrt2)=5 \\ now\\ h(5)=\)

and you can finish it

let b be the number of dollars that my brother has

let m be the number orf dollars that I have

since giving 5 dollars makes the values same meaning that m-5 = b+5

now he gives me 25 dollars and i have twice as much that he has so: 2(b-25) = m+25 or 2b-50 = m+25. which means that 2b = m+25

simplifying the first equation: b = m-10 and substituting it gives 2(m-10) = m+25 which means that 2m-20 = m+25. So i have 45 dollars. The question wants my brothers dollar amount, so we can substitute 45 for m into any equation and find that my brother has 35 dollars

By telescoping sums, this is equal to 1/3.

the correct answer is 13. 

you can go from A to D then go to B then C which is

5+3+5

it is incorrect but good try!

Since ∠PAQ = 13°, then ∠QAP = 90 - 13 = 77°.

Since AQ is an angle bisector, then ∠BAQ = ∠QAP/2 = 38.5°.

Since AR is a median, then ∠BAR = ∠BAC/2 = 45°.

Since ∠B > ∠C, then ∠BAC = 90 - ∠C.

Therefore, ∠C = 45°.

Therefore, ∠RAC = ∠BAR - ∠BAQ = 45 - 38.5 = 6.5°.

Let the constants be A and B, so 1/(n(n + 3)) = A/n + B/(n + 3).

We can solve for A and B by multiplying both sides of the equation by n(n + 3), then combining like terms. We get:

A(n + 3) + Bn = 1

We can solve for A and B by setting n = 0 and n = -3, respectively. When n = 0, the left-hand side of the equation is 0, so we have:

A(3) + B(0) = 1

This gives us A = 1/3. When n = -3, the left-hand side of the equation is 1, so we have:

A(-2) + B(-3) = 1

This gives us B = -1/6. Therefore, A = 1/3 and B = -1/6, and we have:

1/(n(n + 3)) = 1/3n - 1/6(n + 3)

How does 1/4 =1/3+1/3, and how does 1/7= 1/3- 2/3^2?

\(\frac{3x + 12}{x + 4} = (4x^2 + 8x + 18x^2)(2x)\)

\(3=(4x^2 + 8x + 18x^2)(2x)\)

\(3=(2x)(22x^2+8x)\)

\(3=44x^3+16x^2\)

I'm afraid that's as far as I can get you.

There is no such number. I went through and tried all of the possible numbers, none of them work.

Here is a short way to do so: If the digits are within 4 of each other, then the number's reversal will be too close. However, if they are 6 or above away from each other, the number's reversal will be too far away. So the digits must be 5 apart. Since the first digit must be larger, the possibilities are 50,61,72,83, and 94. None of these match the last requirement, so there is no such number.