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2A=1+1/2+1/22+.....+1/29
2A-A=(1+1/2+1/22+....+1/29)-(1/2+1/22+1/23+...+1/210 )
A=1-1/210
=1024/1024-1/1024
=1023/1024
Vậy A = 1023/1024
Ta có : 2A = \(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
2A A = \(\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)
A = \(1-\frac{1}{2^{10}}=\frac{1023}{1024}\)
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{10}}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{1024}=\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{512}-\frac{1}{1024}\)
\(A=\frac{1}{2}-\frac{1}{1024}=\frac{511}{1024}\)
b)Ghi đầu baì
=(1+2+3+...+100).(12+22+32+....+1002).(65.111-13.555)
=(1+2+3+...+100).(12+22+32+....+1002).(65.111-13.5.111)
=(1+2+3+...+100).(12+22+32+....+1002).(111.(65-65))
=(1+2+3+...+100).(12+22+32+....+1002).111.0
=(1+2+3+...+100).(12+22+32+....+1002).0
=0
A = 1002 + 2002 + 3002 + ... + 9002 + 10002
A = 1002.(12 + 22 + 32 + ... + 92 + 102)
A = 10000.385
A = 3850000
Tính nhanh:
a) (1+2+3+..+100) x (12 +22+32+...+...102) x ( 65.111-13.15.37)
b)19x64+76x34
c)12x35+65x13
a Ta có
(1+2+3....+100).(1^2+2^2+..+10^2).(13.5.3.37-13.15.37)
=(1+2...+100).(1^2+2^2+...+10^2).0=0
b Ta co
19.64+76.34=19.4.16+76.34=76.16+76.34=76(16+34)=76.50=3100 ( cau c tuong tu )
A=1+21+22+23+...+210
2A=21+22+23+24+...+211
2A-A=21+22+23+24+...+211-(1+21+22+23+...+210)
A=211-1
A= 2048-1
A= 2047
A = 20 + 21 + 22 + ... + 210
2A = 21 + 22 + 23 + ... + 211
2A - A = (21 + 22 + 23 + ... + 211) - (20 + 21 + 22 + ... + 210)
A = 211 - 20
A = 2048 - 1 = 2047