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Finger [1]
3 years ago
8

Prove that the sum of all natural numbers is -1/12.

Mathematics
1 answer:
ankoles [38]3 years ago
5 0
This is not true. The infinite series


\displaystyle\sum_{n=1}^\infty n

converges if and only if the sequence of its partial sums converges. The k-th partial sum is

\displaystyle\sum_{n=1}^kn=\frac{k(k+1)}2

but clearly this diverges as k gets arbitrarily large.
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Write the expanded form of 9,003,840,165
Tanya [424]
9,000,000,000 + 3,000,000 +800,000 +40,000 + 100 + 60 +5 

~ Here you go (/>ω<)/
6 0
3 years ago
Read 2 more answers
Suppose that $3000 is placed in an account that pays 16% interest compounded each year. Assume that no withdrawals are made from
Papessa [141]

Answer:

a) $3480

b) $4036.8

Step-by-step explanation:

The compound interest formula is given by:

A(t) = P(1 + \frac{r}{n})^{nt}

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Suppose that $3000 is placed in an account that pays 16% interest compounded each year.

This means, respectively, that P = 3000, r = 0.16, n = 1

So

A(t) = P(1 + \frac{r}{n})^{nt}

A(t) = 3000(1 + \frac{0.16}{1})^{t}

A(t) = 3000(1.16)^{t}

(a) Find the amount in the account at the end of 1 year.

This is A(1).

A(t) = 3000(1.16)^{t}

A(1) = 3000(1.16)^{1} = 3480

(b) Find the amount in the account at the end of 2 years.

This is A(2).

A(2) = 3000(1.16)^{2} = 4036.8

4 0
3 years ago
In the diagram, angle 1 = 4x + 30, and angle 3 = 2x +48.
iragen [17]

Answer:

Since we have the information for Angles 1 and 3, and they are vertical, we can set them equal to each other. Once we have done this we can find the measures of them combined, and subtract it from 360 in order to only have the measure of 2 and its vertical angle. Finally, all we need to do now is divide the remaining measure by 2, and this will give us the measure of angle 2.

Angle 1=Angle 3

4x+30=2x+48

2x+30=48

2x=18

x=9

Angle 1=4(9)+30

Angle 1=36+30

Angle 1=66

Angle 1=Angle 3

Angle 1+ Angle 3=132

360-132=228

228/2=114

Angle 2= 114

6 0
3 years ago
The linear equation was solved using these steps.
NISA [10]

Answer:

what are the options

Step-by-step explanation:

????????????????????????????????

3 0
3 years ago
Y = x + 2<br> y = 3x - 4
exis [7]

Answer:

x=3; y=5

Step-by-step explanation:

y=x+2

y=3x-4

so x+2=3x-4

2x=6

x=3

because y=x+2

                  x=3

so y=3+2

     =5

8 0
3 years ago
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