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\(B=1+2+4+...+4096\)
\(B=1+2+2^2+2^3+...+2^{12}\)
\(2B=2+2^2+...+2^{13}\)
\(2B-B=\left(2+2^2+...+2^{13}\right)-\left(1+2+...+2^{12}\right)\)
\(B=2^{13}-1\)
B=1+2+4+8+...+4098
B=\(1+2+2^2+2^3+....+2^{12}\)
2B=\(2+2^2+2^3+2^4+.....+2^{13}\)
2B-B=\(\left(2+2^2+2^3+2^4+...+2^{13}\right)-\left(1+2+2^2+2^3...+2^{12}\right)\)
B=\(2^{13}-1\)
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a; 100 - 94 + 90 - 84 + 80 - 74 + 70 - 64 + 60 - 54
= (100 - 94) + (90 - 84) + (80 - 74) + (70 - 64) + (60 - 54)
= 6 + 6 + 6 + 6 + 6
A = 6 x 5
A = 30
b; 5.125.20.16
= (5.20). (125.8).2
= 100.1000.2
= 200000
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a) \(\frac{15}{16}\cdot\frac{4}{3}-\frac{1}{2}:\frac{5}{4}+3\)
\(=\frac{5}{4}-\frac{2}{5}+3\)
\(=\frac{25}{20}-\frac{8}{20}+\frac{60}{20}\)
\(=\frac{77}{20}=3\frac{17}{20}\)
b) \(\left(\frac{2}{3}-\frac{3}{8}\right):\left(\frac{3}{5}+\frac{1}{4}\right)\)
\(=\frac{7}{24}:\frac{17}{20}\)
\(=\frac{35}{102}\)
c) \(\frac{15}{8}\cdot\left(\frac{1}{3}+\frac{1}{8}\right)-\frac{3}{8}:\frac{3}{4}\)
\(=\frac{15}{8}\cdot\frac{11}{24}-\frac{1}{2}\)
\(=\frac{55}{64}-\frac{1}{2}\)
\(=\frac{23}{64}\)
d) \(\frac{20}{21}:\left(\frac{4}{5}-\frac{1}{10}\right)+\frac{13}{15}:\frac{5}{26}\)
\(=\frac{20}{21}:\frac{7}{10}+\frac{52}{15}\)
\(=\frac{200}{147}+\frac{52}{15}\)
\(=4\frac{608}{735}\)