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18.03.2013

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ab + cd, a2 + b2 = 1, c2 + d2 = 1 ac + bd = 0?

: ab + cd = 0. .

: , e = (a,b) f = (c,d) .
e = (cos φ, sin φ), f = (cos ψ, sin ψ), |φ - ψ| = π/2. , ψ = φ + π/2. f = (-sin φ, cos φ). ab + cd = 0.


1/13 + 1/35 + ... + 1/(2n - 1)(2n + 1), nN.

: 1/k(k + 2) = 1/2(1/k - 1/(k + 2)).

: n/(2n + 1).


0/1 + 1/2! + 2/3! + ... + (n - 1)/n!, nN.

: (k - 1)/! = 1/(k - 1)! - 1/!.

: 1 - 1/n!.


11! + 22! + 33! + ... nn!, nN.

: k!k = (k + 1)! - k!.

: (n + 1)! - 1.


, p q , x10 + px7 + q = 0 .

: , x , .

: , x - , .. x = 2n (nZ). :
(2n)10 + (2n)7p + q = 0. , - , - . . - . . x .
, x - , .. x = 2n + 1 (nZ). :
(2n + 1)10 + (2n + 1)7p + q = 0. , - , , - . - . - . . x - . , x , . , x - .
.


a , 4x2 - 15x + 4a = 0 .

: .

: a = -125/8, a = 27/8.


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