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\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}+\frac{1}{2^8}+\frac{1}{2^9}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^7}+\frac{1}{2^8}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^8}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}\right)\)
\(A=1-\frac{1}{2^9}\)
Vậy \(A=1-\frac{1}{2^9}\)
a)\(\left(10^2+11^2+12^2\right)\div\left(13^2+14^2\right)\)
\(=\left(100+121+144\right)\div\left(169+196\right)\)
\(=365\div365\)
\(=1\)
b) \(1.2.3...9-1.2.3...8-1.2.3...8^2\)
\(=1.2.3...8\left(9-1-8\right)\)
\(=1.2.3...8.0\)
\(=0\)
d) \(1152-\left(374+1152\right)+\left(-65+374\right)\)
\(=1152-374-1152-65+374\)
\(=\left(1152-1152\right)-65+\left(374-374\right)\)
\(=0-65+0\)
\(=-65\)
e) \(13-12+11+10-9+8-7-6+5-4+3+2-1\)
\(=13-\left(12-11\right)+\left(10-9\right)+\left(8-7\right)-\left(6-5\right)-\left(4-3\right)\)\(+\left(2-1\right)\)
\(=13-1+1+1-1-1+1\)
\(=13+0+0+0\)
\(=13\)
a,113-3+20
=1328+20
=1348
b,300+7781+1425
=9506
c,7+36-40
=43-40=3
a,
115 : 112 - 33 : ( 11 + 23 ) + 22 x 30 x 5
= 11( 5 - 2 ) - 27 : ( 1 + 8 ) + 4 x 1 x 5
= 113 - 27 : 9 + 4 x 5
= 1331 - 3 + 20
= 1328 + 20
= 1348
b,
12 x 25 + 31 x 251 + 57x 25
= 12 x 25 + 57 x 25 + 31 x 251
= ( 12 + 57 ) x 25 + 31 x 251
= 69 x 25 + 31 x 251
= 1725 + 7781
= 9506
c,
15 - 23 + 4 x 32 - 5 x 8
= 15 - 8 + 4 x 9 - 40
= 15 - 8 + 36 - 40
= 7 + 36 - 40
= 43 - 40
= 3