1、-()1 2 3 4 2.1 . . . . (). .ann, .1.1 , (, , ), .:1. :2. :3. : (n, an). , 4. :1. 10000, 2%. , .2. , (). , () (Fibonacci 1170-1250Leonardo)1, 1, 2, 3, 5, 8, 13, 21, 34, -. , .1.2 A = a1, a2, L, D(delta):Da1 = a2 - a1,Da2 = a3 - a2,Da3 = a4 - a3, L, nDan = an+1 - an,D, -ADA, DAD2A =D2an, D2an = D(Dan)
2、 = Dan+1 - Dan= an+2 - an+1 - an+1 + an= an+2 - 2an+1 + an,A, D2anD3an, , Dan.:, , ., . , .A =an =22322, 22352, 22401, 22456, 22479, 22511,DA = Dan = 30, 49, 55, 23, 32,. an = 3n - 5, n = 1, 2, 3, L. , .1.1 cbn = 1, 2, 3, L an = cn + b,: 1. n, an;2. -ann, .1.2 Dan = c, cn, an(b an = cn + b). , .1.3
3、an, : , D2an = c.1.4 an: nD2an = c, c, , .: , kk+1, , ank+1, k an = 1, 3, 6, 10, 15, 21, L, Dan = 2, 3, 4, 5, 6, LD2an = 1, 1, 1, 1, 1, L. an = An2 + Bn + C, an = n2 = 12, 22, 32, 42, 52, 62, LnSn, n. DSn=(n+1)2=22, 32, 42, 52, L,D2Sn =2n+3 = 5, 7, 9, 11, LD3Sn = 2, 2, 2, 2, L Sn = An3 + Bn2 + Cn +
4、D.S1 = 1, S2 = 5, S3 = 14, S4 = 30A + B + C + D =1,8A +4B + 2C + D =5(23 A +22 B +2C + D =5),27A + 9B + 3C + D =14(33A + 32B + 3C + D =14),64A + 16B+ 4C + D =30(43A + 42 B+ 4C + D =30),A, B, CDA = 1/3, B = 1/2, C = 1/6, D = 0,. 1.3 A = ank, ak ak+1(, Dak 0).Ak, ak ak+1(Dak 0).Ak, ak ak+1ak ? ak-1(,
5、Dak-1 ? 0Dak 0).Ak, ak ak+1ak ? ak-1(Dak-1 ? 0Dak 0).Ak, Dak Dak-1(, D2ak-1 0).Ak, Dak Dak-1(D2ak-1 0).: k-1k. : , .1.4 Ak, D2akD2ak-1. n2 - 4n + 3 an = n2 - 4n + 37, , , . . 2.1 , . .2.2 (an), , , , . . , .2.3 , ., , -.(). , , , , (, ): , .2 : , , 2.4 ., 7% an+1 = an + 0.07an, ann.2.5 , , . an+1 =
6、an + 0.07anak = (0.07)kc, c, :2.6 , .ak = (0.07)kcan+1 = an + 0.07an, ca0.: . . . , k, . . , , . , . 2.1 an+1 = ran + br ? 1. an = bn + c, r = 1.3 (). , .4 . , -.: , , , , , -(), .: , , , .: , .4.1 -.-: (), . , P, Q, D, S, nn. Pnn, Qnn. , , (4.1)Pn. (4.1). :1. , n n-1Pn-1, 2. , nPn, Pn, , , 3. , , (
7、4.2)(4.3)(4.4)(4.5), .(4.5)(4.5)(4.5)A. (4.6)(4.5):1. b d, t?+(, PnP*, P*;2. b = d, P0, P1, P2, L, Pn, LP*,;3. b d, t?+(, Pn.a2 = 130.68, b2 = 139.22,a7 = 142, b7 = 128,a14 = 146, b14 = 126,a30 = 147, b30 = 123,tn(2), t:1. a2 - 4b 0. (3)t1, t2. (2)C1C2.2. a2 - 4b = 0. (3)t1. (2)AB.3. a2 - 4b 0. (3)(2)AB(1), a* = C, (1). nan, . ABn.anr(r?1), a1 = a, Snn, . AB.n. S1 = a1 = a, S2 = a1 + a2 = a(1 + r), AB, , ., , , , .: : : :; , . , ?, . A, 1, 2, 3, L, n, (), .8(1), (2), :-: 64: 65 5, 8, 13, :(), ?