Let an and BN satisfy A1 = B1 = 6, A2 = B2 = 4, A3 = B3 = 3, and a (n + 1) - an (n belongs to positive integer) is an arithmetic sequence Let an and BN satisfy A1 = B1 = 6, A2 = B2 = 4, A3 = B3 = 3, and a (n + 1) - an (n is a positive integer) is an arithmetic sequence, Sn is the sum of the first several terms of the sequence {BN}, and Sn = 2n-bn + 101) is the general term formula of an and BN (2) Does K belong to a positive integer, so that AK BK belongs to (0,1 / 2)? If so, find K; if not, explain the reason

Let an and BN satisfy A1 = B1 = 6, A2 = B2 = 4, A3 = B3 = 3, and a (n + 1) - an (n belongs to positive integer) is an arithmetic sequence Let an and BN satisfy A1 = B1 = 6, A2 = B2 = 4, A3 = B3 = 3, and a (n + 1) - an (n is a positive integer) is an arithmetic sequence, Sn is the sum of the first several terms of the sequence {BN}, and Sn = 2n-bn + 101) is the general term formula of an and BN (2) Does K belong to a positive integer, so that AK BK belongs to (0,1 / 2)? If so, find K; if not, explain the reason

A (n + 1) - A (n) = a + (n-1) Da = a (2) - A (1) = 4-6 = - 2A + D = a (3) - A (2) = 3-4 = - 1D = - 1-A = 1a (n + 1) - A (n) = - 2 + n-1 = n-3a (n + 1) - (1 / 2) (n + 1) ^ 2 - A (n) + (1 / 2) n ^ 2 = a (n + 1) - A (n) - (2n + 1) / 2 = n-3 - (2n + 1) / 2 = - 7 / 2 {a (n) - (1 / 2) n ^ 2} is a (1) - 1 / 2 = 11 /
X1 + x2 + kx3 = - 2; X1 + kx2 + X3 = - 2; kx1 + x2 + X3 = K-3, what is the value of K,
(3) There are infinite solutions and the general solution is obtained
Augmented matrix of equations=
1 1 k -2
1 k 1 -2
k 1 1 k-3
elementary row operations
1 1 k -2
0 k-1 1-k 0
0 1-k 1-k^2 3k-3
elementary row operations
1 1 k -2
0 k-1 1-k 0
0 0 2-k-k^2 3k-3
(1) No solution
Rank of coefficient matrix
In the triangle ABC, the angle a = 90 degrees, ad is perpendicular to D, BC is at D, e is the midpoint of AC, connect ed and extend the extension line of intersection AB and F, prove: ab: AC = DF: AF
It is proved that: ad is perpendicular to D, BC is perpendicular to D, e is the midpoint of AC, so de = EC = 1 / 2 * AC, angle c = EDC, angle BAC = 90 degrees, ad is perpendicular to D, so angle c = angle bad, angle EDC = angle FDB, angle FDB = angle bad, angle f = angle F, so triangle AFD is similar to triangle DBF, so AF / DF = ad / BD, angle abd = angle abd, angle bad = angle ACD, so triangle abd is similar to triangle CAD, so AC / AB = ad / BD, AC / AB = AF / DF, so AB * AF = AC * DF
Let f (x) be differentiable at x0, then for any constant a, B, LIM (H → 0) [f (x0 + ah) - f (x0 BH)] / h=
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Two arithmetic sequences {an}, {BN}, a1 + A2 + +anb1+b2+… +If BN = 7n + 2n + 3, then a5b5 = ()
A. 7213B. 7C. 378D. 6512
The sum of the first n terms of the arithmetic sequence {an}, {BN} can be set as Sn and TN respectively, sntn = a1 + A2 + +anb1+b2+… +BN = 7n + 2n + 3, ｜ a5b5 = 2a52b5 = a1 + a9b1 + B9 = 9 (a1 + A9) 29 (B1 + B9) 2 = s9t9 = 7 × 9 + 29 + 3 = 6512, so D is selected
The general solution of solving linear equations 2x1 + x2-x3 + X4 = 1 4x1 + 2x2-2x3 + 2x4 = 2 2x1 + x2-x3-x4 = 1
As shown in the figure, in △ ABC, BD and CE are respectively the midlines on the sides of AC and AB, and extend BD and CE to f and g respectively, so that DF = BD and eg = CE, then the following conclusions are obtained: ① GA = AF, ② GA ‖ BC, ③ AF ‖ BC, ④ g, a and F are on a straight line, and ⑤ A is the midpoint of line GF, where ()
A. 5 B. 4 C. 3 d. 2
In △ AEG and △ BEC, Ge = EC ∠ AEG = ∠ becbe = AE, ≌ AEG ≌ △ BEC, (SAS) ≌ BC = AG, ≌ BCE = ∠ g, ∥ Ag ∥ BC, ② correct; in △ AEG and △ BEC, ad = DC ∠ ADF = ∠ cdbbd = DF, ≌ AEG ≌ △ BEC, (SAS) ≌ BC = AF, ≌ DBC = ∠ F, ∥ AF ∥ BC, ③ positive
The function f (x) is defined at the point x = x0. When x → x0, f (x) has a limit ()
A. Necessary conditions
B. Sufficient conditions
C. Necessary and sufficient conditions
D. Irrelevant conditions
First of all, whether a function has a limit at a certain point has nothing to do with whether it has a definition at that point. Second, even if there is a definition, the sufficient and necessary condition for the existence of a limit is that both the left and right limits exist and are equal
Let d be defined by the limit of F (x) at x0
Choose a
If there is a point (x, y) on the plane, rotate it around the coordinate origin by an angle α, and then calculate the coordinates of the rotated point
The complex coordinate (x + Yi) (COSA + isina) = xcosa ysina + (ycosa + xsina) I
The coordinate is (xcosa ysina, ycosa + xsina)
Find the general solutions of the following linear equations: 2x1 + x2-x3 + X4 = 1,4x1 + 2x2-2x3 + X4 = 2,2x1 + x2-x3-x4 = 1
Augmented matrix=
2 1 -1 1 1
4 2 -2 1 2
2 1 -1 -1 1
r2-2r1,r3-r1
2 1 -1 1 1
0 0 0 -1 0
0 0 0 -2 0
The * (1 / 2) of R1 + R2, r3-2r2, R2 * (- 1)
1 1/2 -1/2 0 1/2
0 0 0 1 0
0 0 0 0 0
The general solution is: (1 / 2,0,0) + C1 (- 1 / 2,1,0,0) + C2 (1 / 2,0,1,0). C1 and C2 are arbitrary constants