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1; 73.52.54.76:(55.78)
= (73.76).(52.54) : (55.78)
= 79.56: (55.78)
= (79:78).(56:55)
= 7.5
= 35
2; 33.a7.3.a2:(34.a6)
= (33.3).(a7.a2): (34.a6)
= 34.a9: (34.a6)
= (34:34).(a9:a6)
= a3
A = 2^3 + 2^4+ 2^5+ 2^6 + 2^7 + ... + 2^90
2A = 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + .... + 2^90 + 2^100
2A - A = ( 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + .... + 2^90 + 2^100 ) - ( 2^3 + 2^4+ 2^5+ 2^6 + 2^7 + ... + 2^90 )
A = 2^100 - 2^3
B = 1 + 5 + 5^2 + 5^3 + 5^4 + .... + 5^50
5B = 5 + 5^2 + 5^3 + 5^4 + 5^5 + .... + 5^50 + 5^51
5B - B = ( 5 + 5^2 + 5^3 + 5^4 + 5^5 + .... + 5^50 + 5^51 ) - ( 1 + 5 + 5^2 + 5^3 + 5^4 + .... + 5^50 )
4B = 5^51 - 1
B = 5^51 - 1 / 4
Bài 1. Rút gọn
a)
\(7^3\cdot5^2\cdot5^4\cdot7^6:(5^5\cdot7^8)\)
\(=7^{3+6}\cdot5^{2+4}:(5^5\cdot7^8)\)
\(=7^9\cdot5^6:(5^5\cdot7^8)\)
\(=7^{9-8}\cdot5^{6-5}\)
\(=7\cdot5\)
\(=35\)
b)
\(3^3\cdot a^7\cdot3\cdot a^2:(3^4\cdot a^6)\)
\(=3^{3+1}\cdot a^{7+2}:(3^4\cdot a^6)\)
\(=3^{4-4}\cdot a^{9-6}\)
\(=1\cdot a^3\)
\(=a^3\)
c)
\(7^3\cdot11^4\cdot a^8\cdot b^7: (7^2\cdot11^2\cdot a^5\cdot b^6)\)
\(=7^{3-2}\cdot11^{4-2}\cdot a^{8-5}\cdot b^{7-6}\)
\(=7\cdot11^2\cdot a^3\cdot b\)
\(=847a^3b\)
d)
\((2^5\cdot a^4\cdot b^3)\cdot(2^3\cdot a\cdot b^5):(2^7\cdot a^3\cdot b^7)\)
\(=2^{5+3}\cdot a^{4+1}\cdot b^{3+5}:(2^7\cdot a^3\cdot b^7)\)
\(=2^{8-7}\cdot a^{5-3}\cdot b^{8-7}\)
\(=2\cdot a^2\cdot b\)
\(=2a^2b\)
a) 23 = 8; 24 = 16; 25 = 32; 26 = 64; 27 = 128; 28 = 256; 29 = 512; 210 = 1024
b) 32 = 9; 33 = 27; 34 = 81; 35 = 243
c) 42 = 16; 43 = 64; 44 = 256
d) 52 = 25; 53 = 125; 54 = 625
c) 62 = 36; 63 = 216; 64 = 1296
a) 23 = 8; 24 = 16; 25 = 32; 26 = 64; 27 = 128; 28 = 256; 29 = 512; 210 = 1024
b) 32 = 9; 33 = 27; 34 = 81; 35 = 243
c) 42 = 16; 43 = 64; 44 = 256
d) 52 = 25; 53 = 125; 54 = 625
e) 62 = 36; 63 = 216; 64 = 1296
HT
a) \(B=2+2^2+2^3+2^4+\cdots+2^{100}\)
Ta có:
\(B=2(1+2+2^2+\cdots+2^{99})\)
\(B=2\cdot\dfrac{2^{100}-1}{2-1}\)
\(B=2(2^{100}-1)\)
\(B=2^{101}-2\)
b) \(C=1+3+3^2+3^3+\cdots+3^{2003}\)
Ta có:
\(C=\dfrac{3^{2004}-1}{3-1}\)
\(C=\dfrac{3^{2004}-1}{2}\)
c) \(D=1+5+5^2+5^3+\cdots+5^{1997}\)
Ta có:
\(D=\dfrac{5^{1998}-1}{5-1}\)
\(\boxed{D=\dfrac{5^{1998}-1}{4}}\)
d) \(E=4+4^2+4^3+\cdots+4^n\)
Ta có:
\(E=4(1+4+4^2+\cdots+4^{n-1})\)
\(E=4\cdot\dfrac{4^n-1}{4-1}\)
\(E=\dfrac{4(4^n-1)}{3}\)
22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64
27 = 128; 28 = 256; 29 = 512; 210 = 1024
32 = 9; 33 = 27; 34 = 81; 35 = 243
42 = 16; 43 = 64; 44 = 256
52 = 25; 53 = 125; 54 = 625
\(\frac{4^5+4^5+4^5}{3^5+3^5+3^5}=\frac{3.4^5}{3.3^5}=\frac{1.4^5}{1.3^5}=\left(\frac{4}{3}\right)^5\)
có phải ko!