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a ) C = 1 + 3 + 32 + 33 + ....... + 320
<=> 3C = 3.( 1 + 3 + 32 + 33 + ...... + 320 )
<=> 3C = 3 + 32 + 33 + 34 + ....... + 321
<=> 3C - C = ( 3 + 32 + 33 + 34 + ....... + 321 ) - ( 1 + 3 + 32 + 33 + ...... + 320 )
<=> 2C = 321 - 1
=> C = ( 321 - 1 ) : 2
b ) B = 2 + 22 + 23 + ...... + 250
<=> 2B = 2.( 2 + 22 + 23 + ...... + 250 )
<=> 2B = 22 + 23 + 24 + ....... + 251
<=> 2B - B = ( 22 + 23 + 24 + ...... + 251 ) - ( 2 + 22 + 23 + ...... + 250 )
=> B = 251 - 2
a, Ta có: 3C=3+3^2+3^3+3^4+...+3^21
3C-C=(3+3^2+3^3+...+3^20+3^21)-(1+3+3^2+...+3^19+3^20)
<=>2C = 3^21 - 1 - 3^20 =3^20. (3-1) -1=3^20 .2 -1
=>C\(=\frac{3^{20}.2-1}{2}=3^{20}-\frac{1}{2}=3^{20}-0,5\)
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5 thành 51
1+1+2+3+4+.......+49+50 rồi tính số số hạng,tìm tổng.cuối cùng +1
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Vì A = 2^50+2^49+2^48+...+2^2+2+1
Suy ra: 2A=2^51+2^50+2^49+...+2^3+2^2+2
A=(2^51+2^50+2^49+...+2^3+2^2+2)-(2^50+2^49+2^48+...+2^2+2+1)
A=2^51-1
2A = 2^51+2^50+....+2^2+2
A = 2A - A = (2^51+2^50+....+2)-(2^50+2^51+....+2+1) = 2^51-1
k mk nha
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2A=251-250+249-248+...+23-22+2
=>2A+A=251-250+249-248+...+23-22+2+250-249+248-247+...+22-2+1
=>3A=251-1
=>A=\(\frac{2^{51}-1}{3}\)
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