a=1+2+22+23+...+29
=>2a=2+22+23+24+...+210
=>a=2a-a=(2+22+23+24+...+210)-(1+2+22+23+...+29)
=210-1=1024-1=1023
Vậy a<1024
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Chứng minh:1/2-1/4+1/8-1/16+1/32-1/64+1/128-1/256+1/512-1/1024<1/3
18 tháng 3 2023 lúc 19:38
chứng minh rằng
a , \(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+...+\dfrac{1}{512}-\dfrac{1}{1024}\) < \(\dfrac{1}{3}\)
b , \(\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}\) < \(\dfrac{3}{16}\)
lam vay co duoc ko
1/2+1/4+1/8+... +1/512+1/1024=1-1/2+1/2-1/4+...+1/512-1/1024=1-1/1024=1/1023
tính nhanh ;
1234.5678.(630 -315) :1996
319.45+ 55.319 /1995.1996 -1991.1995
1988.1996+1997.11+1985 /1997.1996-1995.1996
(1+2+4+8+.....+512) .(101.102-101.101-50-51) /2+4+6+8+16+....+1024+2048
(1+2+4+8+....+512).(135135.246-246246.135)/2+4+8+16+....+1024+2048
1/2+1/4+1/8+...+1/512+1/1024
1/2+3/4+7/8+....+511/512+1023/1024
Tính tổng:
A=(1-1/2)+(1-1/4)+(1-1/8)+...+(1-1/512)+(1+1/1024)
1/2+=1/4+1/8+1/16+...+1/512+1/1024
1/2+1/4+1/8+...+1/512+1/1024