In the sequence {an}, the sum of the first n terms is Sn, and S1, S2,... Sn,... Are equal ratio sequence, whose common ratio Q ≠ 1 Prove: {an} (n ≥ 2) is also an equal ratio sequence Original title

In the sequence {an}, the sum of the first n terms is Sn, and S1, S2,... Sn,... Are equal ratio sequence, whose common ratio Q ≠ 1 Prove: {an} (n ≥ 2) is also an equal ratio sequence Original title

It's too simple. How can it be a zero answer?
It is known that SN is the sum of the first n terms of {an}, and {Sn} is an equal ratio sequence, and the common ratio Q ≠ 1
Then Sn = S1 * q ^ (n-1)
thus
an=Sn-S(n-1)=S1*q^(n-1)-S1*q^(n-2)=(S1-S1*q)*q^(n-2)
Easy to know an / an-1 = q
Then {an} is also an equal ratio sequence
It should be noted that when n = 2, an = S1-S1 * q is the first term, so n ≥ 2 is required
So {an} (n ≥ 2) is also an equal ratio sequence

On a square board with a circumference of 80 cm, saw the largest circle. What is the area of the circle? What is the area of the remaining board
() cm square

80/4=20cm
20 × 20 = 400cm square
400 × 0.785 = 31.4cm square circle
(because the circle is 78.5% of the largest in the square)
400 × 0.215 = 8.6cm square

8-12.9 + 1.1, and those that can be calculated simply should be calculated simply

20.88÷0.8-12.9+1.1
=26.1-12.9+1.1
=26.1-13-1
=12.1

Let x1, X2 Xn is an integer and satisfies the square of X1 + the square of x2 + Square of XN = 99 find the cube of X1 + the cube of x2 + +The cube of XN =?

By. - 1

Xiao Li's new household side length is 80 decimeters of floor tiles to lay the ground, need 200 pieces, if the use of an area of 1 square meters of brick to shop

The area of the room is 0.8 × 0.8 × 200
＝0.64×200
＝128﹙㎡﹚
The number of tiles required is 128 △ 1
= 128 (blocks)
A: 128 tiles are needed

Let x > 0, Y > 0 and 2x + 5Y = 20 (1) find the maximum value of XY (2) find the maximum value of lgx + lgY

1.2x + 5Y = 20, y = 2 / 5 (10-x) substituting xy = x * 2 / 5 (10-x) = 2 / 5 (- x ^ 2 + 10x) = 2 / 5 [- (X-5) ^ 2 + 25] when x = 5, the maximum value of the above formula is 2 / 5 * 25 = 10, so the maximum value of XY is 102. Lgx + lgY = lgxy, because XY takes the maximum value, the maximum value of lgxy is LG10 = 1

The inverse function of y = SiNx, X ∈ [π / 2,3 π / 2]

Y = arcsinx, the domain of the original function is transformed into a range, and the domain of the original function is transformed into a domain, that is, y ∈ (π / 2,3 π / 2)
Then x ∈ (- 1,1)

The surface area of the large cube is______ Square centimeter

Because 33 = 27, the edge length of the assembled large cube is composed of three small cubes, so the edge length of the assembled large cube is 3cm, so the surface area is: 3 × 3 × 6 = 54 (square centimeter). Answer: the surface area of the large cube is 54 square centimeter

The environment-friendly vehicle will serve the 2008 Olympic Games venues. When an environment-friendly vehicle with battery as driving energy runs at a constant speed on the horizontal road, the input current of the driving motor is I = 50a, the voltage is u = 300V, and the resistance of the vehicle is 1.2 × 10 ^ 3
(1) Calculate the input power P of driving motor
(2) If the driving motor can convert 80% of the input power into the mechanical power of the traction vehicle, the distance of the vehicle in one hour can be calculated

(1) P=UI=300*50=15000W
(2) 15000*80%=12000
According to P = FV
12000=1.2×10^3 * V
V=10m/s=36Km/h
36km in one hour

Find the derivative dy / DX of the function determined by the parametric equation. In the braces, x = Sint, y = cos2t

x't=cost
y't=-2sin2t
dy/dx=y't/x't=-2sin2t/cost=-4sintcost/cost=-4sint