What is the sum of 1 + 2 + 3 + 4 +. 1999 + 2000 + 2001?

What is the sum of 1 + 2 + 3 + 4 +. 1999 + 2000 + 2001?

two million three thousand and one

1-2+3-4+5...+1999-2000+2001

Odd number: 1 + 3 + 5 + 7 + 9 +2001 = (1 + 2001) * 1001 / 2 = 1002001 (here are (2001 + 1) / 2 = 1001 items) even number: 2 + 4 + 6 + 8 +2000 = (2 + 2000) * 1000 / 2 = 1001000 (there are (2000 / 2 = 1000 items) because even numbers are negative, so odd sum minus even sum = original answer = 100

As shown in the figure BD = 2cm, AC = 20cm, rotate triangle ABC around AC axis to get a figure, and calculate the volume of the figure

13 × 3.14 × 22 × 20, = 13 × 3.14 × 4 × 20, = 125615 (cubic centimeter). A: the volume of this figure is 125615 cubic centimeter

What is the original function of the function cos (MX) ^ 2 and how to calculate it
As the title!
corrections...
It's cos ^ 2mx

(cosmx)^2=(1+cos2mx)/2
∫(cosmx)^2dx=1/2∫(1+cos2mx)dx
=1/2x+1/2∫(1/2m)cos2mxd2mx
=1/2x+1/4m∫cos2mxd2mx
=1/2x+(1/4m)sin2mx

If a = {x │ x (2x-1) │ > 0, B = {x │ y = log3 (1-x)}, then what is the intersection of a and B

A = {x │ x (2x-1) │ > 0} obtains that a = {x │ x ≠ 1, and X ≠ 1 / 2}
B = {x │ y = log3 (1-x)} has: 3 (1-x) > 0
3(1-x)≠1
The conclusion is: B = {x │ X

As shown in the figure, in square ABCD, e is a point on AB, f is a point on ad extension line, and △ CBE is equal to △ CDF
In the graph, if G is on AD and ∠ GCE = 45 °, is Ge = be + GD true? Why?

All △ CBE is equal to △ CDF
∴BE=DF,∠BCE=∠DCF,EC=FC
And ∠ GCE = 45 degree
∴∠BCE+∠GCD=45°
That is, GCF = 45 degree
∴△ECG≌△FCG
∴EG=FG=DG+DF=DG+BE

Again, how to convert the singular to the plural

For example, when it is an apple. Is converted to plural, they are apples. In the conversion of singular and plural, we should see the pronouns and nouns contained in the sentence, what are their plural forms. Of course, when we modify the noun pronouns, we should also make corresponding changes to their predicates and quantifiers

The locus of the center of a circle passing through known points m and N is

Connect two points m and N, make the vertical bisector of Mn, and the center of the circle moves on the vertical bisector. Because the distance from the center of the circle to two points is equal, the distance from the point on the vertical bisector of the line segment to two points is equal, so it is on the vertical bisector

Find the indefinite integral of ∫ (e ^ x-1) ^ (- 1 / 2),
That's [(e ^ x) - 1] ^ (- 1 / 2)

Let u & # 178; = e ^ X - 1 = > 2udu = (e ^ x) DX
∫ (e^x - 1)^(-1/2) dx = ∫ dx/√(e^x - 1)
= ∫ 1/u • 2udu/(u² + 1)
= 2∫ du/(u² + 1)
= 2arctan(u) + C
= 2arctan√(e^x - 1) + C

English translation
To assess reproducibility,30 cephalometric radiographs
were redigitized,and 30 sets of study casts
were rescored 1 week after the initial scoring.

To assess reproducibility, 30 X-ray photographs of head measurements were taken
At the same time, 30 sets of molds have been verified
They were scored again a week after the first score,