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\(N=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{10^2}\)
\(N>\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{10.11}\)
\(N>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....-\frac{1}{11}=\frac{1}{2}-\frac{1}{11}=\frac{10}{22}>\frac{9}{22}\)
Vậy N > 9/22
A = \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\)
2 \(\times\) A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\)
2 \(\times\) A - A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) - (\(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\))
A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) - \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) - \(\dfrac{1}{8}\) - \(\dfrac{1}{16}\) - \(\dfrac{1}{32}\)
A = 1 - \(\dfrac{1}{32}\)
A = \(\dfrac{31}{32}\)
A = 1 + 4 + 9 + 16 +....+ 64 + 81 + 100
=>A = 1 + 1 + 3 + 1 + 8 +...+ 1 + 63 + 1 + 80 + 1 + 99
=>A = 1 + 1 + ..... + 1 + 3 + 8 + 14 +....+80 + 99
Bạn tự tìm kết quả nhé
Hok tốt
A=(1+9)+(4+16)+(9+81)+(16+64)+(25+36+49+100)
A=10+20+90+80+(61+49+100)
A=10+20+90+80+110+100
A=(100+10)+(20+90)+80+110
A=110+110+110+80
A=(110.3)+80
A=330+80
A=410
t i c k cho mình nha
bạnnnnnnnnnnnnnnnnnnnnn
\(\frac{1}{5}+\frac{4}{10}+\frac{9}{15}+\frac{16}{20}+1+\frac{36}{30}+\frac{49}{35}+\frac{64}{40}+\frac{81}{45}\)
\(=\left(\frac{1}{5}+\frac{81}{45}\right)+\left(\frac{4}{10}+\frac{49}{35}\right)+\left(\frac{9}{15}+\frac{49}{35}\right)+\left(\frac{16}{20}+\frac{36}{30}\right)+1\)
\(=2+2+2+2+1\)
\(=2\times4+1\)
\(=9\)
~ Hok tốt ~
a)
Vì 2/9=6/27=8/36=12/54=16/72=18/81 nên:
2/9+6/27+8/36+12/54+16/72+18/81=
2/9+2/9+2/9+2/9+2/9+2/9=
2/9*6=
12/9=
4/3
Vậy 2/9+6/27+8/36+12/54+16/72+18/81=4/3
b)
Ta có:
1-2/5=3/5
1-2/7=5/7
1-2/9=7/9
...
1-2/99=97/99
Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=
3/5*5/7*7/9*...*97/99=
(3*5*7*...*97)/(5*7*9*...*99)=
3/99=
1/33
Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=1/33
c)
Gọi biểu thức 1/2+1/4+1/8+1/16+...+1/1024 là S,ta có:
S=1/2+1/4+1/8+1/16+...+1/1024
S*2=1+1/2+1/4+1/8+...+1/512
S*2-S=(1+1/2+1/4+1/8+...+1/512)-(1/2+1/4+1/8+1/16+...+1/1024)
S=1-1/1024
S=1023/1024
Vậy 1/2+1/4+1/8+1/16+...+1/1024=1023/1024
b: A=1/3+1/9+...+1/3^10
=>3A=1+1/3+...+1/3^9
=>A*2=1-1/3^10=(3^10-1)/3^10
=>A=(3^10-1)/(2*3^10)
c: C=3/2+3/8+3/32+3/128+3/512
=>4C=6+3/2+...+3/128
=>3C=6-3/512
=>C=1023/512
d: A=1/2+...+1/256
=>2A=1+1/2+...+1/128
=>A=1-1/256=255/256
Ta thấy quy luật :
1 = 1x1
4 = 2x2
9 = 3x3
16 = 4x4
....
81 = 9x9
100
=> Các số là : 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100
Tổng là : ( 1 + 9 ) + ( 4 + 16 ) + 25 + ( 36 + 64 ) + ( 49 + 81 ) + 100
= 10 + 20 + 25 + 100 + 130 + 100
= 385
Tổng = 385
Không biết đúng k nữa
sakura bn có thể tham khảo bài này mà làm nè
Ta có :1x1 + 2x2 + 3x3+ 4x4 + 5x5 +6x6+ 7x7 + 8x8 + 9x9
Vậy sẽ là : 1+4+9+16+25+36+49+64+81
Vậy sẽ là : [ 1+9] + [4+36] + [81+49] + [64+16] + 25
10 + 40 + 130 + 80 + 25 = 285
Vậy tổng dãy số đó là 285
có j` tick mình nhé