tinh H=1/5+1/5^2+1/5^3+...+1/5^2008
tinh nhanh
a) 36*17-8.7*25+64*17-0.87*650
b) 2009*14+1994+2007*2008/2008+2008*505+504*2008
c) 1*1+2*2+3*3+4*4+5*5+...+98*98
b) \(\frac{2009.14+1994+2007.2008}{2008+2008.505+2008.504}\)
\(=\frac{\left(2008+1\right).14+1994+2007.2008}{2008.\left(1+505+504\right)}\)
\(=\frac{2008.14+14+1994+2007.2008}{2008.1010}\)
\(=\frac{2008.14+14+1994+2007.2008}{2008.1010}\)
\(=\frac{2008.14+2008+2007.2008}{2008.1010}\)
\(=\frac{2008.\left(14+1+2007\right)}{2008.1010}\)
\(=\frac{2008.2022}{2008.1010}=\frac{1011}{505}\)
c) 1 . 1 + 2 . 2 + 3 . 3 + 4 . 4 + 5 . 5 + ... + 98 . 98
= 1 . ( 2 - 1 ) + 2 . ( 3 - 1 ) + 3 . ( 4 - 1 ) + 4 . ( 5 - 1 ) + 5 . ( 6 - 1 ) + ... + 98 . ( 99 - 1 )
= 1 . 2 - 1 + 2 . 3 - 2 + 3 . 4 - 3 + 4 . 5 - 4 + 5 . 6 - 5 + ... + 98 . 99 - 98
= ( 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 + 5 . 6 + ... + 98 . 99 ) - ( 1 + 2 + 3 + 4 + 5 + ... + 98 )
đặt A = 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 + 5 . 6 + ... + 98 . 99
3A = 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + 4 . 5 . 3 + 5 . 6 . 3 + ... + 98 . 99 . 3
3A = 1 .2 . 3 + 2 . 3 . ( 4 - 1 ) + 3 . 4 . ( 5 - 2 ) + 5 . 6 . ( 7 - 4 ) + ... + 98 . 99 . ( 100 - 97 )
3A = 1 . 2 . 3 + 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + 5 . 6 . 7 - 4 . 5 . 6 + ... + 98 . 99 . 100 -97 . 98 . 99
3A = 98 . 99 . 100
A = 98 . 99 . 100 : 3
A = 323400
đặt B = 1 + 2 + 3 + ... + 98
Số số hạng của B là :
( 98 - 1 ) : 1 + 1 = 98 ( số hạng )
Tổng B là :
( 98 + 1 ) . 98 : 2 = 4851
Thay A , B vào ta được :
323400 - 4851 = 318549
36 . 17 - 8,7 . 25 + 64 . 17 - 0,87 . 650
= ( 36 . 17 + 64 . 17 ) - ( 8,7 . 25 + 0,87 . 650 )
= 17 . ( 36 + 64 ) - ( 8,7 . 25 + 8,7 . 65 )
= 17 . 100 - 8,7 . ( 25 + 65 )
= 17 . 100 - 8,7 . 90
= 1700 - 783
= 917
1. 3/2/3+ 1/1/5 - 2/5/3 + 5/3/5
2. 1/2+ 1/6 + 1/12+ 1/20 + 1/30+ 1/42
3. 3/5 = 13-x/ x+11
4.12x + x45 = 468
5.Cho A = 2007/2008 + 2008/2009 + 2009/2010
Cho B = 2007 + 2008 + 2009/ 2008 + 2009 +2010
Hãy so sánh A và B.
Các bạn giúp mk với nhé, Mk căm ơn rất nhiều!!!!!!!
tinh A=1-2+3+4-5-6+7+8-9-...+2007+2008-2009-2010
A=1 + (-2+3)+(4-5)+(-6+7)+(8-9)+....+(-2006+2007)+(2008-2009)-2010
A=1+1-1+1-1+....+1-1-2010
A=1-2010 = -2009
Đáp số: A=-2009
tính tổng 1/5^2+1/5^3+1/5^4+.............+1/5^2008
2008+2007/2+2006/3+2005/4+2005/5+........................3/2006+2/2007+1/2008
1/2+1/3+1/4+1/5+....................+1/2009
2008-1/2008=2007/2008
1/2-1/2009=2007/2009
2008+2007/2+2006/3+2005/4+2005/5+........................3/2006+2/2007+1/2008
1/2+1/3+1/4+1/5+....................+1/2009
chung minh rang
A = 1/5+1/5^2+1/5^3+...+1/5^2008<1/4
tinh tong
a)s=1+(-2)+3+(-4)+.......+2009+(-2010)
b)s=1+(-2)+(-3)+4+5+6(-6)+(-7)+......+2008+2009+(-2010)
Bài 5:1/2+1/3+...+1/2008).x=2009/1+2010/2+2011/3+5016/2008-2008