The problem of the summation of high order sequence Given that the sequence {an} satisfies an = n + 1 (n is odd) an = 2 ^ n (n is even), and the sum of the first n terms of the sequence {an} is Sn, find SN

The problem of the summation of high order sequence Given that the sequence {an} satisfies an = n + 1 (n is odd) an = 2 ^ n (n is even), and the sum of the first n terms of the sequence {an} is Sn, find SN

An = n + 1 (n is odd) an = 2 ^ n (n is even),
As two sequences
an=n+1
a(n-2)=n-2+1=n-1
So the tolerance of odd items is 2
Even term an = 2 ^ n
a(n-2)=2^(n-2)
So the common ratio of even terms is 4
When n is odd
Sn=(a1+a3+a5+...+an)+（a2+a4+a6+a8+...+a(n-1)）
=[(2+n+1)(n+1)/2]/2+4[1-4^(n-1)/2]/(1-4)
=(n+2)(n+3)/2+4/3*[4^(n-1)/2-1]
When n is an even number term
Sn=[a1+a2+a3+.+a(n-1)]+[a2+a4+a6+a8+...+an]
=[(2+n-1)(n/2)]/2+[4(1-4^(n/2)]/(1-4)
=n(n+1)/4+4/3*[4^(n/2)-1]

The whole poem of the wanderer's chant

You Zi Yin (Tang) Meng Jiao's mother has thread in her hand, and you Zi's coat. When you leave, you are afraid of coming back late. Who said that cuncao's heart is rewarded by sanchunhui? Notes (1) Yin: recite. (2) you Zi: a person who travels far away. In this poem, you refer to Meng Jiao. (3) Lin: about to come. (4) fear: worry. (5) return: come back, go home. (6) words: say (7) cuncao: Hemerocallis

Mathematics problem of grade two in junior high school
It is known that the image of the first-order function y = KX + B intersects with the image of the inverse scale function y = - 8 / X at two points a and B, and the abscissa of point a and the ordinate of point B are - 2
To find: (1) the analytic formula of the first-order function;
(2) According to the image, write the value range of X that makes the value of the first function smaller than that of the inverse function
To detailed process ha ~ good answer to add [20 points]!

(1) When x = - 2, y = - 8 / (- 2) = 4, then the abscissa of point a is (- 2,4)
When y = - 2, x = - 8 / (- 2) = 4, then the abscissa of point B is (4, - 2)
Then, when x = - 2, y = 4, the equations {4 = - 2K + b k = - 1
When x = 4, y = - 2, - 2 = 4K + B solves the equations and {B = 2}
The analytic formula is y = - x + 2
（2）-x+2

The surface area of a cuboid is 78 square centimeters, the length is 5 centimeters, and the perimeter of its bottom is 16 centimeters

The perimeter of the bottom surface is 16. This bottom surface must contain 5cm side length. If not, the area of the four sides is 16 * 5, which is larger than the total surface area
It can be concluded that the other side of the bottom is 3
The area of the bottom is 15
Except the bottom and the top, the remaining area is 78-2 * 15 = 48
Height is equal to the remaining area divided by the perimeter of the bottom 48 / 16 = 3
Volume equals 5 * 3 * 3 = 45 (cubic centimeter)

Evaluation: sin14 π 3 + cos (− 25 π 4)=______ ．

Sin14 π 3 + cos (− 25 π 4) = sin (4 π + 2 π 3) + cos (6 π + π 4) = sin2 π 3 + cos π 4 = 3 + 22

If positive numbers a and B are two real roots of the equation x & # 178; - 7x + 10 = 0, then the value of LGA + LGB is: please help me solve it,

x²-7x＋10=0
(x-5)(x-2) = 0
x1 =5
x2 =2
lga + lgb
= lg5 + lg2
= lg(5 × 2)
= lg10
= 1

It is known that the coordinates of the intersection point of the image of the first-order function y = KX + B and the inverse scale function y = K / X are (2,3), and the analytic expression of this function is obtained

Y = K / X over (2,3)
k=xy=2*3=6
y=6x+b
Substituting (2,3) into
3=6*2+b,b=-9
So y = 6x-9

The product of one number multiplied by 0.8 is 7 less than 45 0.6. What's the number?

Let this number be x, 0.8x = 0.6 × 45-70.8x = 27-70.8x = 20 & nbsp; & nbsp; X = 25; or: (0.6 × 45-7) △ 0.8 = (27-7) △ 0.8 = 25; answer: this number is 25

For a differentiable function f (x) on R satisfying (X-2) f '(x) greater than or equal to 0, then () a.f (0) + F (4) > 2F (2)
If f (x) satisfies (X-2) f '(x) is greater than or equal to 0, then ()
A. F (0) + F (4) > 2F (2) B. f (0) + F (4) greater than or equal to 2F (2) C. f (0) + F (4)

B. F (0) + F (4) greater than or equal to 2F (2)
∵(x-2)f'(x)≥0
x> 2, f '(x) ≥ 0, f (x) does not decrease ≥ function
∴f(4)≥f(2) ①
x

What's 19 out of 20 △ 9

1) (19 / 20) 18 / 9
=18/(19/20)x(1/9)
=(18x20)/19x(1/9)
=2x20/19
=40/19
2) 20 (18 / 19) △ 9
=(18/19)/20x(1/9)
=[18/(19x20)]x(1/9)
=1/(19x10)
=1/190