D·y c¸c sè viÕt theo quy luËt Bµi 1: T×m sè h¹ng thø n cña c¸c d·y sè sau:
a) 3, 8, 15, 24, 35,
b) 3, 24, 63, 120, 195,
c) 1, 3, 6, 10, 15,
d) 2, 5, 10, 17, 26,
e) 6, 14, 24, 36, 50,
f) 4, 28, 70, 130, 208,
g) 2, 5, 9, 14, 20,
h) 3, 6, 10, 15, 21,
i) 2, 8, 20, 40, 70,
HD:
a) n(n+2)
b) (3n-2)3n
c) ( 1)
2
n n+
d) 1+n2
e) n(n+5)
f) (3n-2)(3n+1)
g) ( 3)
2
n n+
h) ( 1)( 2)
2
n+ n+
i) ( 1)( 2)
2
n n+ n+
Bµi 2: TÝnh:
A = 1.2+2.3+3.4+ +99.100
HD:
3A = 1.2.3+2.3(4-1)+3.4.(5-2)+ +99.100.(101-98)
3A = 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+ +99.100.101-98.99.100
3A = 99.100.101
Bµi 3: TÝnh:
A = 1.3+2.4+3.5+ +99.101
HD:
A = 1(2+1)+2(3+1)+3(4+1)+ +99(100+1)
A = 1.2+1+2.3+2+3.4+3+ +99.100+99
A = (1.2+2.3+3.4+ +99.100)+(1+2+3+ +99)
Bµi 4: TÝnh:
A = 1.4+2.5+3.6+ +99.102
HD:
A = 1(2+2)+2(3+2)+3(4+2)+ +99(100+2)
A = 1.2+1.2+2.3+2.2+3.4+3.2+ +99.100+99.2
A = (1.2+2.3+3.4+ +99.100)+2(1+2+3+ +99)
Bµi 5: TÝnh:
Trang 2A = 4+12+24+40+ +19404+19800
HD:
1
2 A = 1.2+2.3+3.4+4.5+ +98.99+99.100
Bµi 6: TÝnh:
A = 1+3+6+10+ +4851+4950
HD:
2A = 1.2+2.3+3.4+ +99.100
Bµi 7: TÝnh:
A = 6+16+30+48+ +19600+19998
HD:
2A = 1.3+2.4+3.5+ +99.101
Bµi 8: TÝnh:
A = 2+5+9+14+ +4949+5049
HD:
2A = 1.4+2.5+3.6+ +99.102
Bµi 9: TÝnh:
A = 1.2.3+2.3.4+3.4.5+ +98.99.100
HD:
4A = 1.2.3.4+2.3.4(5-1)+3.4.5.(6-2)+ +98.99.100.(101-97)
4A = 1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+ +98.99.100.101-97.98.99.100 4A = 98.99.100.101
Bµi 10: TÝnh:
A = 12+22+32+ +992+1002
HD:
A = 1+2(1+1)+3(2+1)+ +99(98+1)+100(99+1)
A = 1+1.2+2+2.3+3+ +98.99+99+99.100+100
A = (1.2+2.3+3.4+ +99.100)+(1+2+3+ +99+100)
Bµi 11: TÝnh:
A = 22+42+62+ +982+1002
HD:
A = 22(12+22+32+ +492+502)
Bµi 12: TÝnh:
A = 12+32+52+ +972+992
HD:
A = (12+22+32+ +992+1002)-(22+42+62+ +982+1002)
A = (12+22+32+ +992+1002)-22(12+22+32+ +492+502)
Bµi 13: TÝnh:
A = 12-22+32-42+ +992-1002
HD:
A = (12+22+32+ +992+1002)-2(22+42+62+ +982+1002)
Bµi 14: TÝnh:
A = 1.22+2.32+3.42+ +98.992
HD:
A = 1.2(3-1)+2.3(4-1)+3.4(5-1)+ +98.99(100-1)
Trang 3A = 1.2.3-1.2+2.3.4-2.3+3.4.5-3.4+ +98.99.100-98.99
A = (1.2.3+2.3.4+3.4.5+ +98.99.100)-(1.2+2.3+3.4+ +98.99)
Bµi 15: TÝnh:
A = 1.3+3.5+5.7+ +97.99+99.100
HD:
A = 1(1+2)+3(3+2)+5(5+2)+ +97(97+2)+99(99+2)
A = (12+32+52+ +972+992)+2(1+3+5+ +97+99)
Bµi 16: TÝnh:
A = 2.4+4.6+6.8+ +98.100+100.102
HD:
A = 2(2+2)+4(4+2)+6(6+2)+ +98(98+2)+100(100+2)
A = (22+42+62+ +982+1002)+4(1+2+3+ +49+50)
Bµi 17: TÝnh:
A = 13+23+33+ +993+1003
HD:
A = 12(1+0)+22(1+1)+32(2+1)+ +992(98+1)+1002(99+1)
A = (1.22+2.32+3.42+ +98.992+99.1002)+(12+22+32+ +992+1002)
Bµi 18: TÝnh:
A = 23+43+63+ +983+1003
Bµi 19: TÝnh:
A = 13+33+53+ +973+993
Bµi 20: TÝnh:
A = 13-23+33-43+ +993-1003