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a, 100 + 98 + 96 + ... + 2 - 97 - 95 - 93 - ... - 1
= (100 + 98 + 96 + ... + 2) - (97 + 95 + 93 + ... + 1)
= 2550 - 2401
= 149
b, đặt A = 2 + 22 + 23 + ... + 2100
2A = 22 + 23 + 24 + ... + 2101
2A - A = (22 + 23 + 24 + ... + 2101) - (2 + 22 + 23 + ... + 2100)
A = 2101 - 2
c, 3.32.33....3100
= 31 + 2 + 3 + ... + 100
= 35050
\(S=6^2\left(1^2+2^2+3^2+...+10^2\right)=36.385=13860\)
34.(15-10)+15.(10-34)
=34.5+15.(-24)
=170+(-360)
=-190
b.3.(-5)^2+2.(-5)-20
=3.25+-10-20
= 75+-10-20
=45
K nha
a) 34.(15-10)+15.(10-34) b)\(3.\left(-5\right)^2+2.\left(-5\right)-20\)
=3*25-10-20
=75-10-20
=45
=34.5+15.(-24)
=170-360
=-190
S1 = \(1+2+2^2+2^3+...+2^{62}+2^{63}\)
2 . S1 = \(2+2^2+2^3+2^4+...+2^{63}+2^{64}\)
2.S1 - S1 =\(\left(2+2^2+2^3+2^4+...+2^{63}+2^{64}\right)-\left(1+2+2^2+2^3+...+2^{62}+2^{63}\right)\)
S1 = \(2^{64}-1\)
\(S=1+2+2^2+2^3+...+2^{62}+2^{63}\)
\(2S=2+2^2+2^3+2^4+...+2^{63}+2^{64}\)
\(2S-S=2^{64}-1\)
\(S=2^{64}-1\)
1. a) \(45x-37=53\)
\(45x=90\)
\(x=2\)
vay \(x=2\)
b) \(\frac{x}{9}+500=600\)
\(\frac{x}{9}=100\)
\(\frac{x}{9}=\frac{900}{9}\)
\(\Rightarrow x=900\)
vay \(x=900\)
c) \(576-x=139\)
\(x=576-139\)
\(x=437\)
vay \(x=437\)
d) \(\left(48+x\right)-27=79\)
\(48+x=79+27\)
\(48+x=106\)
\(x=58\)
vay \(x=58\)
2. \(2^5.2^7.2^9=2^{5+7+9}=2^{21}\)
\(3^9.3^2.3=3^{9+2+1}=3^{12}\)
\(10^9:10^7=10^{10-7}=10^3\)
3). \(2.2.2.2.2.2=2^6\)
\(2.3.2.2.3.3.3=2^3.3^4\)
\(10.9.10.10.10.9.9=10^4.9^3\)
1 a) x= 720
b ) x=chín trăm
c)x= 437
d)x=58
bài2 a)= 221 b)312 c ) =102
bài 3 a)=26 b)=22 nhân 34 c )= 103 nhân chín mũ 3
S dau tien ne ta có (2016-1):2=1007,5 => ghép được 1007 cap va thua ra 1 so
ta có :(1-2)+(3-4)+........+(2015-2016)+2014
=-1+-1+-1+......+-1+2014
=-1007+2014=1007
B=1+3+3^2+3^3+...+3^100
3B=3+3^2+3^3+3^4+...+3^101
3B-B=3+3^2+3^3+3^4+...+3^101-1-3-3^2-3^3-...-3^100
2B=3^101-1
B=(3^101-1):2
\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
\(\Rightarrow2S=6+3+\frac{3}{2}+....+\frac{3}{2^8}\)
\(\Rightarrow2S-S=\left(6+3+\frac{3}{2}+....+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+....+\frac{3}{2^9}\right)\)
\(\Rightarrow S=6-\frac{3}{2^9}=\frac{3069}{512}\)
\(S=1+2+2^2+2^3+...+2^{10}\)
\(S=1+2\left(2+2^2+...+2^9\right)\)
\(S=1+2\left(S-2^{10}\right)\)
\(S=1+2S-2^{11}\)
\(S=2^{11}-1\)
2S= 2+22+....+211
2S-S=(2+22+....+211)-(1+2+....+210)
S=211 - 1
dễm