What's the fifth of the sixth

What's the fifth of the sixth

This one needs to be regulated
You look at 1 3 / 4 5 / 9 7 / 16 first
The numbers on the denominator are listed as
1 4 9 16
So the nth number on the denominator is the square of n
Looking at molecules 1 3 5 7
So the nth number on the molecule is 2N-1
So find the rules
The nth number is (2n-1) / N ^ 2
The answer must be right
I hope it can help you
You can keep asking me if you don't know

1 3 5 7 9 11 the nth number is
All I know is 2n-
Please say a few words and give the reason
To say reason 1!

2n-1
2*1-1=1
2*2-1=3
2*3-1=5

1, - 3,5, - 7,9, - 11 find the nth number

The answer is: the nth number is [(- 1) ^ (n + 1)] * (2n-1)
N starts with 1

(- 1 / 2) 4 cubic

1/16

Please tell me the formula for calculating the number of multilayered triangles

Number of sides = (n-2) * 3
Number of edges = number of edges / 3 + 2

Is there a general formula between the line segment in a triangle and the number of triangles it contains? What is it?
0 1 2 3 4 ...
1 3 6 10 15 ...
(Note: if there is no line segment in a triangle, then the number of triangles is one; if there is one line segment, then three triangles will appear; as shown above, there is a one-to-one correspondence. Is there any rule between the number of line segments drawn in a triangle and the number of triangles? If so, under what circumstances will the above rule appear?

In some cases, there is a rule
Under such conditions, the relationship between the number of triangles and the number of triangles in the triangle is two order arithmetic sequence, that is, the relationship between the number of triangles y and the number of line segments x is y = x * x / 2 + 3x / 2 + 1
If the line segment does not intersect the vertex, the above formula does not hold and there is no general term expression

The formula of the number of line segments from one vertex and the number of triangles in a triangle angle

Number of triangles = n + 1 (n is the number of line segments from one vertex)
It is equivalent to cutting one knife and two sections
Two triangles in a line

We give the following definition: if there is a quadrilateral in which the sum of squares of two adjacent sides is equal to the square of a diagonal, then the quadrilateral is called a Pythagorean quadrilateral
A quadrilateral is called a Pythagorean quadrilateral if the sum of squares of two adjacent sides is equal to the square of a diagonal. We give the following definition: a quadrilateral is called a Pythagorean quadrilateral if the sum of squares of two adjacent sides is equal to the square of a diagonal, and the two adjacent sides are called the Pythagorean sides of the quadrilateral
(1) Write down the names of the two kinds of special quadrilaterals you have learned, which are Pythagorean quadrilaterals,
(2) As shown in figure (1), given the lattice points (the vertex of the small square) O (0,0), a (3,0), B (0,4), please draw a Pythagorean quadrilateral oamb with the lattice point as the vertex, OA, ob as the Pythagorean edge and the diagonal line equal, and write the coordinates of M
(3) (3) take sides AB and AC of triangle ABC as sides, make square ABDE and acfg to the outside of triangle, connect CE and BG. Compared with point O, P is any point on line De, and prove that quadrilateral obpe is Pythagorean quadrilateral

1) Fill square, rectangle;
(2) As shown in the picture,
(3) It is proved that ∵ △ abd is an equilateral triangle,
∴AB=AD,∠ABD=60°,
∵∠CBE=60°,
∴∠ABD+∠DBC=∠CBE+∠DBC,
That is, ABC = DBE,
And ∵ be = BC,
∴△ABC≌△DBE,
∴BE=BC,AC=ED；
If EC is connected, then △ BCE is an equilateral triangle,
∴BC=CE,∠BCE=60°,
∵∠DCB=30°,
∴∠DCE=90°,
In RT △ DCE,
DC2+CE2=DE2,
∴DC2+BC2=AC2．

It is known that the sum of squares of one set of opposite sides of a quadrilateral is equal to the sum of squares of another set of opposite sides

Let a quadrilateral ABCD be connected with AC to make AE ⊥ BD, CF ⊥ BD, from ab & sup2; + CD & sup2; = ad & sup2; + BC & sup2;
If be & sup2; + DF & sup2; = BF & sup2; + de & sup2; E and f coincide with Pythagorean theorem, then AE and CF are a straight line

We give the following definition: if there is a quadrilateral in which the sum of squares of two adjacent sides is equal to the square of a diagonal, then the quadrilateral is called a Pythagorean quadrilateral
A detailed proof is given

(1) (2) the answer is as shown in Figure 3, m (3,4) or m (4,3). (3) it is proved that the connection EC is AC = de and BC = be because of △ ABC ≌ △ DBF, and because ∠ CBE = 60 °, so △ BCE is equilateral triangle, so EC = BC and ∠ BCE = 60 ° because ∠