Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
S = a + a + + a<br />
n<br />
1 2<br />
K<br />
n;<br />
( )<br />
a + a 2a<br />
d n<br />
n<br />
1<br />
+ −1<br />
1<br />
Sn<br />
= n;<br />
Sn<br />
=<br />
n.<br />
2 2<br />
14.2.11. Äåêàðòîâ³ êîîðäèíàòè íà ïëîùèí³<br />
(ðèñ. 14.1 ³ 14.2):<br />
14.2.8. Ãåîìåòðè÷íà ïðîãðåñ³ÿ<br />
b, b , b , , b n<br />
,<br />
K K 1 2 3<br />
K K ( )<br />
n−1<br />
b = bq ; q = b / b = = b / b = b ≠<br />
n 1 2 1 n n−1 1<br />
0<br />
n n− n+<br />
( )<br />
b = b<br />
1b 1<br />
n≥<br />
2 ; bbn = bbn<br />
−<br />
=<br />
S = b1 + b2 + K + b ;<br />
1 2 1<br />
K;<br />
n n<br />
( −1) ( 1−<br />
) ( )<br />
n n<br />
b1 q b1<br />
q<br />
Sn<br />
= nb1<br />
( q = 1)<br />
; Sn<br />
= = q ≠1<br />
.<br />
q−1 1−q<br />
14.2.9. Íåñê³í÷åííî ñïàäíà ãåîìåòðè÷íà ïðîãðåñ³ÿ<br />
( )<br />
b, b , b , K, b , K ; q < 1 b ≠ 0 ;<br />
1 2 3 n<br />
1<br />
Ðèñ. 14.1 Ðèñ. 14.2<br />
x — àáñöèñà òî÷êè M; y — îðäèíàòà òî÷êè M; x, y —<br />
êîîðäèíàòè òî÷êè M (ðèñ. 14.1); OM<br />
uuuur , OM<br />
uuuur (x, y) — âåêòîð;<br />
x — àáñöèñà âåêòîðà OM<br />
uuuur ; y — îðäèíàòà âåêòîðà OM<br />
uuuur ;<br />
x, y — êîîðäèíàòè âåêòîðà OM<br />
uuuur (ðèñ. 14.2).<br />
Çíàêè êîîðäèíàò òî÷êè M ³ âåêòîðà OM<br />
uuuur çîáðàæåíî íà<br />
ðèñ. 14.3.<br />
b1<br />
Sn = b1+ b2<br />
+ K + bn; S = lim Sn;<br />
S =<br />
n→∞<br />
1 − q<br />
.<br />
14.2.10. Á³íîì Íüþòîíà<br />
( ) n 0 n 1 n−1 m n−m m n−1 n−1<br />
n n<br />
a+ b = C a + C a b+ + C a b + + C ab + C b<br />
K K ,<br />
n n n n n<br />
C<br />
m<br />
n<br />
( −1)( −2) K( − + 1)<br />
n n n n m n!<br />
An<br />
= = =<br />
123 ⋅ ⋅ ⋅K⋅m m! n−m ! P<br />
( )<br />
m<br />
n!<br />
An<br />
= n( n−1)( n−2) K ( n− m+ 1)<br />
=<br />
!<br />
,<br />
P = 1⋅2⋅3 ⋅K<br />
⋅ m = m !.<br />
m<br />
( n−<br />
m)<br />
m<br />
m<br />
,<br />
Ðèñ. 14.3<br />
14.3. ÒÐÈÃÎÍÎÌÅÒвß<br />
14.3.1. Îçíà÷åííÿ òðèãîíîìåòðè÷íèõ ôóíêö³é<br />
sin α= y<br />
x<br />
y; cos<br />
x<br />
OM<br />
= α= OM<br />
= (íà îäèíè÷íîìó êîë³<br />
OM =1);<br />
494 495