Design an algorithm to calculate 1 + 3 + 5 + 7 + 9 +. + 49 Is S1, S2 that is not to calculate the number, not to let the arithmetic sequence! How about the first step, how about the second step

Design an algorithm to calculate 1 + 3 + 5 + 7 + 9 +. + 49 Is S1, S2 that is not to calculate the number, not to let the arithmetic sequence! How about the first step, how about the second step

(1 + 49) * 49 / 2 = 1225 like this belongs to the formula of arithmetic sequence summation
Sum = (first number + last number) * number of items / 2

Design an algorithm to calculate 1 + 3 + 5 + 7 + +99

1+3+5+7+… +99
=(1+99)×50÷2
=50×50
=2500

1/2×3+1/3×4+1/5×4…… 1/98×99+1/99×100=?

=98+1/2+1/3+···+1/99
=97+1+1/2+1/3+···+1/99
=97+ln(99)

1+2+3+4+… +1999+2000+1999+… +4+3+2+1
What's the formula

=（1999+1）*（(19991+1)/2)*2
=2000*1000*2
=4000000
Typing is not easy, if satisfied, hope to adopt

The square of parabola y = x-4x-3 intersects with Y-axis at two points a and B, and the vertex is p

Because the parabola y = x ^ 2-4x-3 = (X-2) ^ 2-7,
So p (2, - 7),
And the discriminant = △ = B ^ 2-4ac = 16 + 12 = 28,
So the absolute value of AB = √Δ / a = 2 √ 7,
So the area of triangle PAB is: (1 / 2) * 2 √ 7 * 7 = 7 √ 7

Mass is proportional to density, right?
I heard the teacher say that it is wrong that the density is directly proportional to the mass. Then how about the mass being directly proportional to the density?

Physical density is a property of matter. It does not change with the change of mass and volume
Therefore, it is wrong that the density is proportional to the mass, and it is also wrong that the mass is proportional to the density, because the density of an object with very small mass can be very large. For example, the density of water is one kilogram per cubic meter, but the density of one gram of water is also one kilogram per cubic meter, and the density of one kilogram of water is also one kilogram per cubic meter, Mass is proportional to density
So for the density formula: ρ = m / V
(1) When p is constant, M is proportional to V; (2) when m is constant, P is inversely proportional to V; (3) when V is constant, P is proportional to M
Note: only (1) is correct, and (2) and (3) are wrong. Because the density of the same substance is fixed, it does not change with the change of volume and mass. Therefore, when understanding the physical formula, it is impossible to be divorced from the physical facts, and the relationship between quantities in the physical formula cannot be understood simply from the perspective of mathematics

Simple operation of 51 * 59-59

Original formula = (51-1) × 59 = 50 × 59 = 2950

For a point a (1,2) on the parabola y = 2x ^ 2, find the focal coordinates of the parabola, the Quasilinear equation, and the tangent equation of the parabola at a

Parabola y = 2x ^ 2, i.e. x ^ 2 = 1 / 2x 2p = 1 / 2 P = 1 / 4
Focus coordinate (1 / 8,0) quasilinear equation x = - 1 / 8
Y '= 4x the slope of the tangent of the parabola at a = 4
The tangent equation of parabola at a is Y-2 = 4 (x-1)
That is 4x-y-2 = 0

After two 2-meter-long cylinders with the same bottom area are assembled into a cylinder steel, the surface area is reduced by 0.6 square decimeter. If each cubic decimeter of steel weighs 7.8 kg, how many kg does the assembled steel weigh?

Bottom area: 0.6 △ 2 = 0.3 (square decimeter) 2 m = 20 decimeter volume of cylinder: 0.3 × 20 × 2 = 12 (cubic decimeter) weight: 2 × 7.8 = 93.6 (kg) answer: the weight of the steel after assembly is 93.6 kg

Multiplication law exercises

A × B = B × a (a × b) × C = a × (B × C) (a + b) × C = a × C + B × C