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\(A=1+3+3^2+...+3^{2007}\)
\(\Rightarrow3A=3+3^2+3^3+...+3^{2008}\)
\(\Rightarrow3A-A=\left(3+3^2+3^3+...+3^{2008}\right)-\left(1+3+3^2+...+3^{2007}\right)\)
\(\Rightarrow2A=3+3^2+3^3+...+3^{2008}-1-3-3^2-...-3^{2007}\)
\(\Rightarrow2A=3^{2008}-1\)
\(\Rightarrow2A+1=3^{2008}\)
\(A=1+3+3^2+...+3^{2007}\)
\(\Rightarrow3A=3+3^2+3^3+...+3^{2008}\)
\(\Rightarrow3A-A=\left(3+3^2+3^3+...+3^{2008}\right)-\left(1+3+3^2+...+3^{2007}\right)\)
\(\Rightarrow2A=3+3^2+3^3+...+3^{2008}-1-3-3^2-...-3^{2007}\)
\(\Rightarrow2A=3^{2008}-1\)
\(\Rightarrow2A+1=3^{2008}\)
Nhớ k cho mk nha!!!
3A=3+32+33+....+32008
2A=(3+32+....+32008)-(1+3+...+32007)=32008-1
3A=\(3+3^2+3^3+...+3^{11}\)
3A-A=(\(3+3^2+3^3+...+3^{11}\))-(\(1+3+3^2+...+3^{10}\))
2A=\(3^{11}-1\)
2A+1=\(3^{11}\)
a, \(A=1+2+2^2+2^3+...+2^{100}\)
=> \(2A=2+2^2+2^3+2^4+...+2^{101}\)
=> \(A=2A-A=2^{101}-1\)
=> \(A+1=2^{101}\)
b, \(B=3+3^2+3^3+...+3^{2005}\)
\(3A=3^2+3^3+3^4+....+3^{2006}\)
=> \(2A=3A-A=3^{2006}-3\)
=> \(2A+3=3^{2006}\)là lũy thừa của 3
=> Đpcm
a) Ta có: \(A=1+2+2^2+2^3+.....+2^{100}\)
\(\Rightarrow2A=2+2^2+2^3+........+2^{101}\)
Lấy 2A-A ta có:
\(2A-A=\left(2+2^2+2^3+2^4+.....+2^{101}\right)\)\(-\left(1+2+2^2+2^3+.......+2^{100}\right)\)
\(\Rightarrow A=2^{101}-1\)
\(\Rightarrow A+1=2^{101}-1+1\)
\(\Rightarrow A+1=2^{101}\)
b) Ta có: \(B=3+3^2+3^3+.....+3^{2005}\)
\(\Rightarrow3B=3^2+3^3+3^4+.....+3^{2006}\)
\(\Rightarrow3B-B=\left(3^2+3^3+3^4+....+3^{2006}\right)\)\(-\left(3+3^2+3^3+......+3^{2005}\right)\)
\(\Rightarrow2B=3^{2006}-3\)
\(\Rightarrow2B+3=3^{2006}-3+3\)
\(\Rightarrow2B+3=3^{2006}\)
Vậy 2B+3 là lũy thừa của 3 ĐPCM
1: \(3A=3^2+3^3+3^4+...+3^{2018}\)
\(\Leftrightarrow2A=3^{2018}-3\)
\(\Leftrightarrow2A+3=3^{2018}\) là lũy thừa của 3(ĐPCM)
2: \(2A+3=3^{2018}=\left(3^2\right)^{1009}=9^{1009}\) là lũy thừa của 9
Bg
a) 43 ÷ 25 = (22)3 ÷ 25
= 22.3 ÷ 25
= 26 ÷ 25
= 26 - 5
= 21
= 2
b) 97 ÷ 32 = 97 ÷ 9
= 97 ÷ 91
= 97 - 1
= 96
c) 2.22.23.24. … .2100
= 21 + 2 + 3 + 4 +…+ 100
Đặt A = 1 + 2 + 3 + 4 +…+ 100 (A có 100 số hạng)
=> A = \(\frac{100.\left(100+1\right)}{2}\)
=> A = \(\frac{100.101}{2}\)
=> A = \(\frac{10100}{2}\)
=> A = 5050
Quay lại với đề bài:
= 25050
a ) \(4^3\div2^5=2^6\div2^5=2^1\)
b ) \(9^7\div3^2=9^7\div9=9^6\)
c ) \(2.2^2.2^3.2^4....2^{100}=2^{1+2+3+....+100}\)
Ta có : \(1+2+3+....+100=\frac{\left(100+1\right).100}{2}=5050\)
\(\Rightarrow2^{1+2+3+....+100}=2^{5050}\)
Ta có:\(A=1+3+3^2+3^3+3^4+3^5\)
\(\Rightarrow2A=1+3^2+3^3+3^4+3^5+3^6\)
\(\Rightarrow2A+1=1+3^2+3^3+3^4+3^5+3^6\)+1
\(2A+1=2+3^2+3^3+3^4+3^5+3^6\)
Nhớ chọn cho mình nhé,mình sẽ ủng hộ cho
A = 1+ 3\(^2\) + \(3^3\)+ ....+ \(3^5\)
\(\Leftrightarrow\)3A = 3+ \(3^2\)+\(3^3\)+...+\(3^6\)
\(\Leftrightarrow\)3A _ A = (3 + \(3^2\)+....+\(3^6\)) _ (1+ 3 +... +\(3^5\))
\(\Leftrightarrow\)2A = \(3^6\) _ 1
\(\Leftrightarrow\)2A +1 = \(3^6\)( dạng lũy thừa bậc 6 )