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A=1+2+2^2+.,.,.+2^20
2A=2+2^2+...+2^21
2A-A=(2+2^2+...+2^21)-(1+2+2^2+...+2^20)
A=2^21-1
2A = 2 + 2^2 + 2^3 + ... + 2^20 + 2^21
2A - A = 2 + 2^2 + 2^3 +... +2^21 - 1 - 2 - 2^2 - ...-2^20
=> A = 2^21 - 1
A = 2097152 - 1 =2097151
1. 53 = 5.5.5 = 125
2. 27 = 2.2.2.2.2.2.2 = 128
3. 44 = 4.4.4.4 = 256
4. 73 = 7.7.7 = 343
6. 35 = 243
7. 26 = 64
8. 34 = 81
9. 83 = 512
11. 132 = 169
12. 112 = 121
13. 142 = 196
14. 152 = 225
16. 172 = 289
17. 182 = 324
18. 192 = 361
19. 202 = 400
21. 104 = 10000
22. 105 = 100000
23. 106 = 1000000
24. 107 = 10000000
\(A=\left(\frac{21}{5}-\frac{3}{5}\right):\frac{16}{8}:\frac{9}{10}\)
\(A=\frac{18}{5}:\frac{16}{8}:\frac{9}{10}\)
\(A=\frac{18}{5}\times\frac{8}{16}\times\frac{10}{9}\)
\(A=\frac{9}{5}\times\frac{8}{8}\times\frac{10}{9}\)
\(A=\frac{72}{40}\times\frac{10}{9}\)
\(A=\frac{8}{4}\times\frac{1}{1}\)
\(A=\frac{8}{9}\)
\(B=\left(1\frac{1}{20}+\frac{36}{100}\right):\frac{84}{25}:\left(2+\frac{14}{16}\right)\)
\(B=\left(\frac{21}{20}+\frac{36}{100}\right):\frac{84}{25}:\left(\frac{32}{16}+\frac{14}{16}\right)\)
\(B=\left(\frac{105}{100}+\frac{36}{100}\right):\frac{84}{25}:\frac{46}{16}\)
\(B=\frac{141}{100}:\frac{84}{25}:\frac{46}{16}\)
\(B=\frac{141}{100}\times\frac{25}{84}\times\frac{16}{46}\)
\(B=\frac{141}{4}\times\frac{1}{84}\times\frac{16}{46}\)
\(B=\frac{141}{336}\times\frac{16}{46}\)
\(B=\frac{141}{21}\times\frac{1}{46}\)
\(B=\frac{141}{966}\)
a: \(A=2^2+4^2+...+20^2\)
\(=2^2\left(1^2+2^2+...+10^2\right)\)
\(=4\cdot385=1540\)
b: \(B=\left(12^2+14^2+16^2+18^2+20^2\right)-\left(1^2+3^2+5^2+7^2+9^2\right)\)
\(=\left(12^2-1^2\right)+\left(14^2-3^2\right)+\left(16^2-5^2\right)+\left(18^2-7^2\right)+\left(20^2-9^2\right)\)
\(=\left(12-1\right)\left(12+1\right)+\left(14-3\right)\left(14+3\right)+\left(16-5\right)\left(16+5\right)+\left(18-7\right)\left(18+7\right)+\left(20-9\right)\left(20+9\right)\)
\(=11\left(1+3+5+7+9+12+14+16+18+20\right)\)
\(=11\left(21+21+21+21+21\right)\)
\(=11\cdot21\cdot5=1155\)
a; A = 22 + 42 + 62 + ... + 202
A = 22.(12 + 22 + 32 + ... + 102)
A = 22. 385
A = 4.385
A = 1540