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PT
4
KT
26 tháng 7 2018
\(S=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\)
\(=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)
\(\Rightarrow\)\(3S=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\)
\(\Rightarrow\)\(3S-S=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)\)
\(\Rightarrow\)\(2S=1-\frac{1}{3^7}\)
\(\Rightarrow\)\(S=\frac{1-\frac{1}{3^7}}{2}\)
26 tháng 7 2018
\(S=\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(3S=1+\frac{1}{3}+...+\frac{1}{3^6}\)
\(3S-S=\left(1+\frac{1}{3}+...+\frac{1}{3^6}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)\)
\(2S=1-\frac{1}{3^7}\)
\(S=\frac{1-\frac{1}{3^7}}{2}\)
TA
17 tháng 6 2019
S = 1 + 1/3 + 1/9 + 1/27 +.....+ 1/2187
S x 3 = 3 + 1 + 1/3 + 1/9 + 1/27 +........+ 1/729
S x 3 - S = ( 3 + 1 + 1/3 + 1/9 + 1/27 +........+ 1/729 ) - ( 1 + 1/3 + 1/9 + 1/27 +.....+ 1/2187 )
S x 3 - S = 3 - 1/2187
S x 3 - S = 6560/2187
S = 6560/2187 : 2
Vậy S = 6560/4374
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
25 tháng 7 2018
Câu a
\(S=\frac{3-1}{1x3}+\frac{5-3}{3x5}+\frac{7-5}{5x7}+...+\frac{2019-2017}{2017x2019}.\)
\(S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}=1-\frac{1}{2019}=\frac{2018}{2019}\)
Câu b
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^6}+\frac{1}{3^7}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^5}+\frac{1}{3^6}\)
\(2A=3A-A=1-\frac{1}{3^7}\Rightarrow A=\frac{1}{2}-\frac{1}{2.3^7}\)
LS
10 tháng 7 2018
T = 5.5 + 6.6 + .... + 30.30
T = 5.(6 - 1) + 6.(7-1) + ... + 30.(31 - 1)
T = 5.6 - 5 + 6.7 - 6 + ... + 30.31 - 30
T = (5.6 + 6.7 + ... + 30.31) - (5 + 6 + ... + 30)
Đặt A = 5.6+ 6.7 + ... + 30.31
B = 5 + 6 + ... + 30
Ta có :
3A = 5.6.3 + 6.7.3 + ... + 30.31 . 3
3A = 5.6.(7-4) + 6.7.(8-5) + ... + 30.31.(32-29)
3A = 5.6.7 - 4.5.6 + 6.7.8 - 5.6.7 + ... + 30.31.32 - 29.30.31
3A = (5.6.7 + 6.7.8 + ... + 30.31.32) - (4.5.6 + 5.6.7 + ... + 29.30.31)
3A = 30.31.32 - 4.5.6
3A = 29640
A = 29640 : 3
A = 9880
SSH của B là : (30 - 5) : 1 + 1 = 26 (số hạng)
Tổng B là : (30 + 5) . 26 : 2 =455
=> T = A - B = 9880 - 455 = 9425
c, S = 1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 + 6561
S = (3 + 2187) + (9 + 6561) + (27 + 243) + (81 + 729) + 1
S = 2190 + 6570 + 270 + 810 + 1
S = (2190 + 810) + 6570 + 270 + 1
S = 3000 + 6570 + 270 + 1
S = 9570 + 270 + 1
S = 9840 + 1
S = 9841
Vậy S = 9841
TH
3
16 tháng 3 2016
Đặt A= 1/3+1/9+1/27+1/81+1/243
A= 1/3+1/3^2+1/3^3+1/3^4+1/3^5
3A=1+1/3+1/3^2+1/3^3+1/3^4
3A-A=1+1/3+1/3^2+1/3^3+1/3^4-1/3-1/3^2-1/3^3-1/3^4-1/3^5
2A=1-1/3^5
2A=242/243
A=121/243
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
28 tháng 8 2018
\(3C=\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{27.28.29.30}\)
\(3C=\frac{4-1}{1.2.3.4}+\frac{5-2}{2.3.4.5}+...+\frac{30-27}{27.28.29.30}\)
\(3C=\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{27.28.29}+\frac{1}{28.29.30}\)
\(3C=\frac{1}{1.2.3}-\frac{1}{28.29.30}\Rightarrow C=\left(\frac{1}{1.2.3}-\frac{1}{28.29.30}\right):3\)
\(S=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)
\(3S=3+1+\frac{1}{3}+...+\frac{1}{3^6}\)
\(3S-S=\left(3+1+\frac{1}{3}+...+\frac{1}{3^6}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)\)
\(2S=3-\frac{1}{3^7}\)
\(S=\frac{3-\frac{1}{3^7}}{2}\)
S= 1+ \(\frac{1}{3}\)+ \(\frac{1}{9}\)+...+ \(\frac{1}{729}\)+ \(\frac{1}{2187}\).
=> S= 1+ \(\frac{1}{3}\)+ \(\frac{1}{3^2}\)+...+ \(\frac{1}{3^6}\)+ \(\frac{1}{3^7}\).
=>3S= 3+ 1+ \(\frac{1}{3}\)+...+ \(\frac{1}{3^5}\)+ \(\frac{1}{3^6}\).
=> 3S- S=( 3+ 1+ \(\frac{1}{3}\)+...+ \(\frac{1}{3^5}\)+ \(\frac{1}{3^6}\))-( 1+ \(\frac{1}{3}\)+ \(\frac{1}{3^2}\)+...+ \(\frac{1}{3^6}\)+ \(\frac{1}{3^7}\)).
=> 2S= 3- \(\frac{1}{3^7}\).
=> 2S= 3- \(\frac{1}{2187}\).
=> 2S= \(\frac{6560}{2187}\).
=> S= \(\frac{6560}{2187}\): 2.
=> S= \(\frac{3280}{2187}\).
Vậy S= \(\frac{3280}{2187}\).