DL
1
K
Khách
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23 tháng 1 2017
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
PP
1
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
21 tháng 5 2023
A = \(\dfrac{1}{1\times2}\) + \(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\)+...+ \(\dfrac{1}{2021\times2022}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\)+...+ \(\dfrac{1}{2021}\) - \(\dfrac{1}{2022}\)
A = 1 - \(\dfrac{1}{2022}\)
A = \(\dfrac{2021}{2022}\)
R
3
T
25 tháng 5 2018
Dấu \(.\)là dấu nhân nhé
Ta có :
\(B=\frac{1}{2}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)
\(\Rightarrow B=\frac{1}{2}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}\)
\(\Rightarrow B=\frac{1}{2}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
\(\Rightarrow B=\frac{1}{2}+\frac{1}{7}-\frac{1}{12}\)
\(\Rightarrow B=\frac{42}{84}+\frac{12}{84}-\frac{7}{84}\)
\(\Rightarrow B=\frac{47}{84}\)
K mik nha
TV
1
8 tháng 6 2021
1/128 * 2 = 1/64
1/64 * 2 = 1/32
1/32 * 2 = 1/16
...
1/4 * 2 = 1/2
1/2 * 2 = 1
Mà A chỉ có một số hạng 1/128 nên tính ra được 127/128
NT
Nguyễn thành Đạt
CTVHS
23 tháng 2 2023
\(1\dfrac{4}{5}+2\dfrac{5}{7}+3\dfrac{4}{5}+4\dfrac{5}{7}\)
\(\text{=}\left(1\dfrac{4}{5}+3\dfrac{4}{5}\right)+\left(2\dfrac{5}{7}+4\dfrac{5}{7}\right)\)
\(\text{=}1+3+\left(\dfrac{4}{5}+\dfrac{4}{5}\right)+2+4+\left(\dfrac{5}{7}+\dfrac{5}{7}\right)\)
\(\text{=}10+\dfrac{8}{5}+\dfrac{10}{7}\text{=}131\dfrac{1}{35}\)
HL
27 tháng 5 2019
a)1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72+89/90
=1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90
=9 – (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=9 – [1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+1/(9x10)]
=9 – ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)
=9 – (1 – 1/10) = 9 – 9/10 = 81/10
b)4/3.7 + 4/7.11 + 4/11.15 + 4/15.19 + 4/19.23 + 4/23.27
=4.(4/3.7 + 4/7.11 + ........+ 4/23.27 )
=1.( 1/3.7 + 1/7.11 + ......+ 1/23.27 )
=1.(1/3 - 1/7 + 1/7 - 1/11 +............ + 1/23 - 1/27 )
=1.(1/3 - 1/27 )
=1.(9/27 - 1/27)
=1.8/27
=8/27
c)1/10+1/40+1/88+1/154+1/138+1/340
=1/2.5 + 1/5.8 + 1/11.8 + 1/11.14 + 1/14.17 + 1/17.20
=1/3. (3/2.5 + 3/5.8 + 3/8.11 + 3/11.14 + 3/14.17 + 3/17.20 )
=1/3. ( 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 + 1/14 - 1/17 + 1/17 -1/20 )
=1/3. ( 1/2 - 1/20 )
=1/3. 9/20
=3/20
P/S: CHÚC HOK TỐT !
PP
2
KV
21 tháng 5 2023
1/(1×2) + 1/(2×3) + 1/(3×4) + ... + 1/(2021×2022)
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2021 - 1/2022
= 1 - 1/2022
= 2021/2022
A = \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+....+\dfrac{1}{72}+\dfrac{1}{90}\)
A = \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+........+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
A = \(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+..+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
A = 1-1/10
A = 9/10