Sum, Sn = 1 + 11 + 111 + 1111 + +(n 1)

Sum, Sn = 1 + 11 + 111 + 1111 + +(n 1)

An=1+10+100+.+10^(n-1)=[10^n-1]/(10-1)
=1/9 * 10^n-1/9
Sn=A1+A2+...+An
=10/9×(10^n-1)/(10-1) - 1/9×n
=10/81×(10^n-1)- 1/9×n

If f (x) = 12 / x + 4x, (1) when x > 0, find the minimum value of F (x) (2) when x

(1) When x > 0, f (x) = 12 / x + 4x ≥ 2 and root (12 / X × 4x)
=2 and root 48 = 8 and root 3
If and only if 12 / x = 4x, that is, x = root 3, the equal sign is taken
That is: the minimum value of F (x) = 8 and the root sign is 3
(2) When x

The relationship between voltage, current and resistance? What formula?

Resistance: resistance is the element that blocks current. The relationship between current, voltage and resistance is called Ohm's law. Definition: the current in resistance is directly proportional to voltage and inversely proportional to resistance. Formula: u = IR, I = u / R, u-voltage,

Creative questions with difficulty in fraction reduction
Simplify X & sup2; + 2x-8 / X & sup3; + 2x & sup2; △ X-2 / X △ x + 4 / x + 1
Questions have requirements, to simplify the solution out with any number to bring in 2

The original formula = [(x + 4) (X-2) / X & sup2; (x + 2)] × [x / (X-2)] × [(x + 1) / (x + 4)]
=[x(x+1)(x+4)(x-2)/[x²(x+2)(x-2)(x+4)]
=(x+1)/[x(x+2)]
=(x+1)/(x²+2x)

The resistance of a water heater is 22 ohm. When it is connected to a 220 V circuit, what is its power? What is the current in the circuit? How many kilowatts of electricity is it used to work for 10 hours?

According to the formula I = u / r = 220 / 22 = 10a,
According to the formula P = UI = 220 * 10 = 2200W / h
Working 10 hours of electric energy Q = Pt = 2200 * 10 = 22 kW = 22 kWh

Simplify 16-8x + x ^ 2-x ^ 2-2x + 1 (1) under root

Because 10,
So IX -- 1I = x -- 1, I4 -- xi = 4 -- X,
So root (16 -- 8x + x ^ 2) -- root (x ^ 2 -- 2x + 1)
=Root (4 -- x) ^ 2 -- root (X -- 1) ^ 2
=I4--xI--Ix--1I
=(4--x)--(x--1)
=4--x--x+1
=5--2x.

When "220 V, 220 W" electrical appliances are connected to 110 V power supply, what is the current passing through?

If it is a resistor, it should be 0.5A. If it is a large screen color TV with good performance, it may only be a few ma. If it is a single-phase motor, it may be 0.3A or 0.8A

Put two wooden sticks AB (10m long) and CD (6m long) on the wall, where be = 6m and de = 2m. Can you judge which one is steeper? Please give reasons

The reasons are as follows: in RT △ Abe, ∵ e = 90 °, ab = 10m, be = 6m, ∵ AE = AB2 − be2 = 8m, ∵ Tan ∠ B = aebe = 86 = 43; in RT △ CDE, ∵ e = 90 °, CD = 6m, de = 2m, ∵ CE = CD2 − de2 = 42m,