tính nhanh : 98.2 + 96.4 + 961.8
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a , 96 . 4 + 4 . 4 + 96 . 0
= 4 . ( 96 + 4 ) + 0
= 4 . 100
= 400
b , 78 . 5 + 5 . 2
= 5 . ( 78 + 2 )
= 5 . 80
= 5 . 2 . 40
= 10 . 40
= 100
c , 5 . 2 + 8 . 9
= 10 + 72
= 82
4.2 +6.2+8.2+10.2+....+96.2+98.2
=2.(4+6+8+10+...+96+98)
Ta có Số số hạng từ 4 đến 98 là:
(98-4):2+1=48(số hạng)
Tổng dãy số trên là:
(98+4).48:2=2448
Vậy ta có được dãy số trên là:2.2448=4896
1.99+2.98+3.97+...+98.2+99.1=1.99+2.(99-1)+3.(99-2)+...+98.(99-97)+99.(99-98)
=1.99+2.99-1.2+3.99-2.3+...+98.99-97.98+99.99-98.99
=(1.99+2.99+3.99+...+98.99+99.99)-(1.2+2.3+3.4+...+98.99)
=99.(1+2+...+99)-(1.2+2.3+...+98.99)=99.4950-(1.2+2.3+...+98.99)=490050-(1.2+2.3+...+98.99)
đặt A=1.2+2.3+...+98.99
=>3A=1.2.3+2.3.3+...+98.99.3
=1.2.3+2.3.(4-1)+...+98.99.(100-97)
=1.2.3-1.2.3+2.3.4-2.3.4+...+97.98.99-97.98.99+98.99.100=98.99.100
=>A=98.99.100:3=323400
=>1.99+2.98+3.97+...+98.2+99.1=490050-323400=166650
1.99+2.98+3.97+4.96+...+98.2+99.1
=1.99+2.(99-1)+3.(99-2)+...+98.(99-97)+99.(99-98)
=1.99+2.99-1.2+3.99-2.3+...+98.99-97.98+99.99-98.99
=(1.99+2.99+3.99+4.99+...+98.99+99.99)-(1.2+2.3+3.4+...+97.98+98.99)
=(1+2+3+4+...+98+99).99-(98.99.100)/3
={(99-1+1)/2}.100.99-(98.99.100)/3
=49,5.100.99-(98.99.100)/3
=4950.99-(98.99.100)/3
=4950.3.33-98.100.33
B=14850.33-9800.33
B=(14850-9800).33
B=5050.33
B=166650
A bài thầy Phú
Ta có: N=1.99+2.98+3.97+..+98.2
=(99-98).99+(99-97).98+(99-96).97+..+(99-1).2
=99.99-98.99+98.99-97.98+99.97-96.97+..+99.2-1.2
=99.99+99.98+99.97+..+99.2-(99.98+98.97+97.96+..+1.2)
=99.(99+98+97+..+2)-323400 (cm a)
Xét dãy 99+98+97+..+2
SSH:(99-2):1+1=98
Tổng: (99+2).98:2=4949
=>N=99.4949-323400
=489951-323400=166551
1.99+2.98+3.97+...+98.2+99.1=1.99+2.(99-1)+3.(99-2)+...+98.(99-97)+99.(99-98)
=1.99+2.99-1.2+3.99-2.3+...+98.99-97.98+99.99-98.99
=(1.99+2.99+3.99+...+98.99+99.99)-(1.2+2.3+3.4+...+98.99)
=99.(1+2+...+99)-(1.2+2.3+...+98.99)=99.4950-(1.2+2.3+...+98.99)=490050-(1.2+2.3+...+98.99)
đặt A=1.2+2.3+...+98.99
=>3A=1.2.3+2.3.3+...+98.99.3
=1.2.3+2.3.(4-1)+...+98.99.(100-97)
=1.2.3-1.2.3+2.3.4-2.3.4+...+97.98.99-97.98.99+98.99.100=98.99.100
=>A=98.99.100:3=323400
=>1.99+2.98+3.97+...+98.2+99.1=490050-323400=166650
S = (50 -49)(50 +49) + (50 - 48)(50 + 48) + .... + (50 + 48)(50 -48)
S = 502 - 492 + 502 - 482 + ..... + 502 - 482 + 502 - 49
S = 99 . 502 - 2.(02 + 12 +.... + 492)
=1.99+2.(99-1)+3.(99-2)+...+98.(99-97)+99(99-98)
=99.(1+2+3+4+...+98+99)-(2+2.3+3.4+...+97.98+98.99)
=99.(1+99).99/2-98.99.100/3
=99.50.99-98.33.100
=490050-323400
=166650
tính nhanh : 98.2 + 96.4 + 961.8
= 98.2 + 961.8 + 96.4
=(98.2 + 961.8) + 96.4
=1060+96.4
=1256.4