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1 tháng 12 2017
\(A=\frac{11.9^{11}.3^7-27^{10}}{\left(2.3^{14}\right)^2}\)
\(A=\frac{11.3^{22}.3^7-3^{30}}{2^2.3^{28}}\)
\(A=\frac{11.3^{29}-3^{30}}{4.3^{28}}\)
\(A=\frac{3^{29}.\left(11-3\right)}{4.3^{28}}\)
\(A=\frac{3.8}{4}\)
\(A=\frac{24}{4}\)
\(A=6\)
vậy \(A=6\)
học tôt Ngô Thị Diệu Linh
TP
1
28 tháng 7 2015
\(A=3^0+3^1+3^2+3^3+3^4+....+3^{2014}\)
\(A.3=\left(3^0+3^1+3^2+3^3+3^4+....+3^{2014}\right).3\)
\(A.3=3^1+3^2+3^3+3^4+....+3^{2015}\)
\(A.3=\left(3^0+3^1+3^2+3^3+3^4+.....+3^{2014}\right)+3^{2015}-3\)
\(A.3=A+3^{2015}-3\)
\(A.2=3^{2015}-3\)( CUNG BOT DI A)
\(A=\frac{3^{2015}-3}{2}\)
nhớ **** mình nha
N
29 tháng 9 2017
\(A=3^0+3^1+3^2+......+3^{2018}\)
\(3A=3.\left(3^0+3^1+3^2+.....+3^{2018}\right)\)
\(3A=3^1+3^2+3^3+........+3^{2019}\)
\(3A-A=\left(3^1+3^2+3^3+......+3^{2019}\right)-\left(3^0+3^1+3^2+.....+3^{2018}\right)\)
\(2A=3^{2019}-3^0\)
\(A=\left(3^{2019}-3^0\right):2\)
\(B=6^{10}+6^{11}+6^{12}+....+6^{2012}\)
\(6B=6.\left(6^{10}+6^{11}+6^{12}+.....+6^{2012}\right)\)
\(6B=6^{11}+6^{12}+6^{13}+.......+6^{2013}\)
\(6B-B=\left(6^{11}+6^{12}+6^{13}+......+6^{2013}\right)-\left(6^{10}+6^{11}+6^{12}+.......+6^{2012}\right)\)
\(5B=6^{2013}-6^{10}\)
\(B=\left(6^{2013}-6^{10}\right):5\)
CU
10 tháng 2 2019
phần b tương tự phần a nên em làm câu a và c thôi :
a, \(M=1-2+2^2-2^3+...+2^{2012}\)
\(2M=2-2^2+2^3-2^4+...+2^{2013}\)
\(3M=2^{2013}+1\)
\(M=\frac{2^{2013}+1}{3}\)
c, \(E=2^{100}-2^{99}-2^{98}-...-1\)
\(E=2^{100}-\left(2^{99}+2^{98}+...+1\right)\)
đặt \(A=2^{99}+2^{98}+...+1\)
\(2A=2^{100}+2^{98}+...+2\)
\(2A-A=2^{100}-1\) hay \(A=2^{100}-1\)
ta có :
\(E=2^{100}-\left(2^{100}-1\right)\)
\(E=2^{100}-2^{100}+1=1\)
S
30 tháng 9 2016
A=1+2+22+23+...+22016
2A=2+22+23+24+...+22017
2A-A=(2+22+23+24+...+22017)-(1+2+22+23+...+22016)
A=22017-1
B=1+3+32+33+...+32014
3B=3+32+33+34+...+32015
3B-B=(3+32+33+34+...+32015)-(1+3+32+33+...+32014)
2B=32015-1
B=\(\frac{3^{2015}-1}{2}\)
RM
24 tháng 7 2017
\(A=2^0+2^1+2^2\)\(+2^3+...+\)\(2^{50}\)
\(2A=2+2^2+2^3+...+2^{51}\)
\(2A-A=A=2^{51}-2^0\)
\(B=5+5^2+5^3+...+5^{99}+5^{100}\)
\(5B=5^2+5^3+5^4+...+5^{100}+5^{101}\)
\(5B-B=4B=5^{101}-5\)
\(B=\frac{5^{101}-5}{4}\)
\(C=3-3^2+3^3-3^4+...+\)\(3^{2007}-3^{2008}+3^{2009}-3^{2010}\)
\(3C=3^2-3^3+3^4-3^5+...-3^{2008}+3^{2009}-3^{2010}+3^{2011}\)
\(3C+C=4C=3^{2011}+3\)
\(C=\frac{3^{2011}+3}{4}\)
\(S_{100}=5+5\times9+5\times9^2+5\times9^3+...+5\times9^{99}\)
\(S_{100}=5\times\left(1+9+9^2+9^3+...+9^{99}\right)\)
\(9S_{100}=5\times\left(9+9^2+9^3+...+9^{99}+9^{100}\right)\)
\(9S_{100}-S_{100}=8S_{100}=5\times\left(9^{100}-1\right)\)
\(S_{100}=\frac{5\times\left(9^{100}-1\right)}{8}\)
24 tháng 10 2023
A=20+21+22+23+...++23+...+250250
2�=2+22+23+...+2512A=2+22+23+...+251
2�−�=�=251−202A−A=A=251−20
�=5+52+53+...+599+5100B=5+52+53+...+599+5100
5�=52+53+54+...+5100+51015B=52+53+54+...+5100+5101
5�−�=4�=5101−55B−B=4B=5101−5
�=5101−54B=45101−5
�=3−32+33−34+...+C=3−32+33−34+...+32007−32008+32009−3201032007−32008+32009−32010
3�=32−33+34−35+...−32008+32009−32010+320113C=32−33+34−35+...−32008+32009−32010+32011
3�+�=4�=32011+33C+C=4C=32011+3
�=32011+34C=432011+3
�100=5+5×9+5×92+5×93+...+5×999S100=5+5×9+5×92+5×93+...+5×999
�100=5×(1+9+92+93+...+999)S100=5×(1+9+92+93+...+999)
9�100=5×(9+92+93+...+999+9100)9S100=5×(9+92+93+...+999+9100)
9�100−�100=8�100=5×(9100−1)9S100−S100=8S100=5×(9100−1)
�100=5×(9100−1)8S100=85×(9100−1)
A=30.32.34....32012.32014=30+2+4+...+2012+2014=32(1+2+3+...+1007)
Ta có: 1+2+3+...+1007=1007(1007+1):2=507528
=> A=32.507528=31015056