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Դ:51ߺҽ    :18945    :2013-10-13 9:04:23
ߺҽѼСѧѧȲѡ

Ȳ
һ֪ʶ㣺
1Уһ˳ųɵһСеÿһһΪһΪĩйеĸ
2Ȳ빫һУӵڶÿһǰһIJȣеĽȲУIJ
3ʽ
Ȳеܺ=+ĩ 2
=ĩ- +1
ĩ=+ -1
=ĩ- -1
=ĩ- -1
ȲУܺ=м


1 369201Уждȥ201Ƕ٣
1ΪȲУ=3ĩ=201=3Ըݹʽ
=ĩ- +1,
2ݹʽĩ=+ -1
⣺ =201-3 3+1=67
ĩ=3+3 201-1=603
𣺹67201603

һ
ڵȲ4101622У48Ƕ٣508еĵڼ
: 48286508ǵ85


2 ȫλĺǶ٣
еλǴ100~999900۲100101102998999 һУһΪ1ĵȲСҪͿõȲ͹ʽ
⣺ 100+999 900 2
=1099 900 2
=494550
ȫλĺ494550
һ
12000ȻУż֮֮͵IJ
: 1000

3Ȼб101λĺ͡
һλУ101С1191֪Ȳ11213191ĺ͡9ǿԸ͹ʽ㡣
һ 11+21+31++91
=11+91 9 2
=459

͹ʽóȲ11213191ĺ459ǿ9ƽ459 9=5151ǡȲеĵмһ()ɴֿɵõS= nֻʱȲʽ㡣
11+21+31++91
=51 9
=459
𣺺459
һ
󲻳500б11Ȼĺ͡
: 11385

4 зиĺͣ
12344950
23455051
34565152

495051529798
505152539899
һÿһУУһȲУȷֱÿһУУ֮ͣĺ͡
һ ÿһ֮ͣ
һУ1+50 50 2=1275
ڶУ2+51 50 2=1325
У3+51 50 2=1375

ʮУ49+98 50 2=3675
ʮУ50+99 50 2=3725
֮ͣ
1275+1325+1375++3675+3725
=1275+3725 50 2
=125000

۲ÿһпԿӵڶÿһкͶǰһж50ԿȽһеĺͳ50ټϸбȵһжҲĺ͡
1+50 50 2 50=63750
50 1+2+3++49
=50 1+49 49 2
=61250
63750+61250=125000
ĺ125000
һ
з100ĺ͡
012389
1234910
23451011

91011121718
: 900

5༶аÿҪѡְһΡһ105Σôжμ?
蹲мѡֲμӱֱA A2A3 A An A ʼ˳Σ
A A2 A3A4Anһ1ƣn-1
A2ѺA ֻҪA 3A4 A5 An1ƣn-2
A 3ѺA A2ֻҪA4 A5 A6An 1ƣn-3
ԴƣAn-1ֻܺAn1
⣺ Sn=n-1+n-2++2+1
= 1+n-1 n-1
= n (n-1)
⣬Sn=105()n n-1=210Ϊnͨ㷨֪15 14=210.
n=15,15μ˱
15μ˱
һ
15050ȻУȡӣʹʹ50жͬȡ
𰸣 625

6Χ16ȦһȦһȦȦ6ˣ912ˣȦжˣȦжˣ
֪912Χ16ȦһȦһȦ⵽ڸȦμ6ˣҲǸȲеĺ912166ĿҪǵȲĩ a - a =d (n-1)=6 (16-1)=90()
⣺ a +a =S 2 n=912 2 16=114ˣ
Ȧ=90+114 2=102ˣ
Ȧ=114-90 2=12ˣ
Ȧ102ˣȦ12ˡ
һ
Χ8ȦһȦһȦڸȦ4ˣ304ˣȦмˣ
𰸣 52


ģ 4
һ ÿС5֣
1һ֪һ6ÿһǰ4⴮е2003

2Ȳ03691245еĵ 
2ʼ100żĺ

3һԺ25λӵһԺÿŶǰһŶ2λ2570λԺ λ

4

541λĺ

6ʱÿøӵÿһ£һҹʱһ ¡

7һܹ600飬֪һ㶼һ10顣һ
飬һ 顣

8200500ܱ֮7ĸ֮

91949195019511987198840ȻУż֮ͱ֮Ͷ

10һ1200220011200019991ӵʼÿǰдȥСIJӵһʼ2002Ϊֹ2002ĺ

(ÿС10)
110ֻӣ54ƹܲܰ54ƹŽȥʹӵƹȣ

2СסһͬͬƺŴ1ſʼȥСȫͬƺпͣ110õĽΪ114ôʵȫͬжټң

3һѴϸȵԲľѳͼ״һ7԰ľÿ²1һ95ʣԲľһжٸ


4һεͼһ㣬һ㣬ڶÿ㣬ÿ㡭ε100㣬ʣжٸ㣿



5X+Y+Z=1993ж⣿


ģԣ 4
һ
18014
6+4 2003-1
=6+4 2002
=8014

216
45-0 3+1
=45 3+1
=16

310100
ĩ=2+100+1 2=200
=2+200 100 2=10100

4. 1150
a =70-(25-1) 2=22()
λ22+70 25 2=1150

5123525
г41λΪ101105109997
997-101 4+1=225
ͣ101+997 225 2=123525

6180
1+12 12+1 24
=13 12+24
=180£

7100140
мһ㱾600 5=120
һ㣺12-10 2=100
һ㣺120+1 2=140

815050
ȲΪ203210497
=497-203 7+1=43
к=203+497 43 2=15050

920
1950+1988 20 2-1949+1987 20 2
=3938 20 2-3936 20 2
=39380-39360
=20

101782225
ԭУ1Ϊ־һ飬2002 3=66712001Ϊ667飬6671ΪµһǡΪ12002668120026691334
668 1+2002+669 1334 2
=668+1781557
=1782225



1⣺

Ҫ첻

2⣺110ȷ10-1=9ôȷΪ114-9=105ȫͬƺɵΪ105
ȫͬnңΪ123n
ͣ1+n n 2=105
1+n n=210
210ֽ⣺210=2 3 5 7
=14 15
nΪ14
ȫͬʵ14ҡ

3⣺ 7+95=102
95-7+1=89㣩
102 89 2=4539
Բľһ4539

4⣺100е㣺6+99-1 6
=6+98 6
=6 99
=594
ֻе㣺 1+6+594 99 2
=1+600 99 2
=29701
е29701

5⣺ X=1991ʱY+Z=2 Y=Z=1 1
X=1990ʱY+Z=3 2
X=1989ʱY+Z=4. 3

X=2ʱY+Z=1991 1990
X=1ʱY+Z=1992 1991
Xܵ19921993
ԭвͬ⣬Ϊ
1+2+3+4++1991
=1991 1992 2
=1983036
𣺹1983036⡣







ٶ:СѧѧȲ⾫ѡ

------վԴȨԭУַȨϵǡ

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