Observe the following formula: 2 ^ 1 = 2, 2 ^ 2 = 4, 2 ^ 3 = 8, 2 ^ 4 = 16, 2 ^ 5 = 32, 2 ^ 6 = 64, 2 ^ 7 = 128, 2 ^ 8 = 256. By observing, you can find 2 ^ n Try to write the last number of 2 ^ 2009

Observe the following formula: 2 ^ 1 = 2, 2 ^ 2 = 4, 2 ^ 3 = 8, 2 ^ 4 = 16, 2 ^ 5 = 32, 2 ^ 6 = 64, 2 ^ 7 = 128, 2 ^ 8 = 256. By observing, you can find 2 ^ n Try to write the last number of 2 ^ 2009

Last digit
Rule: 24 8 6 2 4 8 6
The cycle is four
2009/4=502.1
The remainder is one
The last number of 2 ^ 2009 = 2

The general formula of (3 / 2), (1), (5 / 8), (3 / 8), (7 / 32)

(n + 2) / 2 ^ n (n / N of 2 plus 2)

1 - (1 / 6 + 1 / 3), 2-3 / 7 + 4 / 7, 3 / 4-1 / 3-3 / 8, 68-7.5 + 32-2.5, 5 / 12 - (1 / 12-1 / 2) should be calculated

1-(1/6+1/3)=1-3/6=1/2
2-3/7+4/7=14/7-3/7+4/7=15/7
3/4-1/3-3/8=18/24-8/24-9/24=1/24
68-7.5+32-2.5=60.5+32-2.5=92.5-2.5=90
5/12-（1/12-1/2）=5/12-(1/12-6/12) =5/12-(-5/12)=10/12=5/6

The solution of equal ratio sequence
If the general term formula of an is known as an = (- 1) ^ (n + 1) * (4n-3), then the sum of its first 100 terms

S100=(1-5)+(9-13)+.+(393-397)=50×（-4）=-200

-66 by 176-33 by - 68 + 22 by 126

(-66)*176-33*(-68)+22*126
=(-66)*176+(-66)*(-34)-(-66)*42
=(-66)*(176-34-42)
=(-66)*100
=-6600

(1 + x ^ 3) / 2 + 3x + x ^ 2 divide this,

(1+x^3)/(2+3x+x^2 )
=[(x+1)(x^2-x+1)]/[(x+1)(x+2)]
=(x^2-x+1)/(x+2)

How much is 120 times 5 / 8 times 2 / 3

120 × 5 / 8 × 2 / 3
=75 × 2 / 3
=50

Calculation: 4x ^ 3 * x ^ 4-x ^ 9 △ x ^ 2

4x^3*x^4-x^9÷x^2
=4x^7-x^7
=3x^7

64 out of 81

81:64 no more

How to judge the positive and negative of a + C according to the image of quadratic function

Look at two points
When a point is x = - 1
The other point is when x = 1
When x = - 1, there is Y1 = A-B + C
When x = 1, y2 = a + B + C
y1+y2=2a+2c
If both Y1 and Y2 are positive, then a + C is positive
If both Y1 and Y2 are negative, then a + C is negative
If Y1 and Y2 are positive and negative, then the absolute value is larger than the next one