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18.03.2013

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, L, M, N - l-, m-, n- . , L m-nM n-lN l-m = 1.

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L, M, N A q:

L = Aql - 1.

M = Aqm - 1.

N = Aqn - 1.

L m-nM n-lN l-m =

= Amq(l - 1) m / Anq(l - 1) n Anq(m - 1) n / Alq(m - 1) l Alq(n - 1) l / Amq(n - 1) m =

qlm / qln qmn / qml qnl / qnm = 1.

.


, 12, . 12 9, . .

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, a aq. .. 12 , a2q2 = 12a.

a = 12 / q2.

.. a, aq, 9 , 2aq = a + 9.

a(2q - 1) = 9.

a :

12(2q - 1) = 9q2.

3q2 - 8q + 4 = 0.

q1 = 2, q2 = 2/3.

. q = 2 3, 6, 12. q = 2/3 27, 18, 12.

: 3, 6, 12 27, 18, 12.


8. 11 .

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a3 + a9 = a1 + a11 = 8.

S11 = (a1 + a11) 11 / 2 = (a3 + a9) 11 / 2 = 44.

: S11 = 44.


, a2n a2m , a2n /a2m = -1. , ? , ?

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:

a2n + a2m = 0;

, , :

a1 + (2n - 1)d + a1 + (2m - 1)d = 0;

2a1 + 2nd + 2md - 2d = 0;

a1 + (n + m - 1)d = 0.

, a1 d, . .., , an + m = 0.

: , n + m.


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