A = 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^n < 1

A = 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^n

2A = 1 + 1/2 + 1/2^2+ ..+ 1/2^n-1

2A - A = 1 + 1/2 + 1/2^2+ ..+ 1/2^n-1 - (1/2 + 1/2^2 + 1/2^3 + ... + 1/2^n)

A = (1 - 1/2^n) + (1/2 - 1/2) + ..+ (1/2^n-1 -1/2^n-1)

A = 1 - 1/2^n

A < 1 (đpcm)

Câu b:

B = 1/3 + 1/3^2 + 1/3^3 + ...+ 1/3^n < 1/2

3B = 1 + 1/3 + 1/3^2 + ..+ 1/3^n - 1

3B - B = 1 + 1/3 + 1/3^2 + ..+ 1/3^n - 1 - (1/3 + 1/3^2 + 1/3^3 + ...+ 1/3^n)

2B = 1 + 1/3 + 1/3^2 + ..+ 1/3^n - 1 - 1/3 - 1/3^2 - 1/3^3 -..- 1/3^n-1 - 1/3^n

2B = (1 - 1/3^n) + (1/3 - 1/3) +..+(1/3^n-1-1/3^n-1)

2B = 1 - 1/3^n

B = 1/2 - 1/2.3^n < 1/2 (đpcm)

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2 - 1 = 1     3 - 1 = 2     1 + 1 = 2     1 + 2 = 3

3 - 1 = 2     3 - 2 = 1     2 - 1 = 1     3 - 2 = 1

3 - 2 = 1     2 - 1 = 1     3 - 1 = 2     3 - 1 = 2

2 - 1 = 1     3 - 1 = 2     1 + 1 = 2     1 + 2 = 3

3 - 1 = 2     3 - 2 = 1     2 - 1 = 1     3 - 2 = 1

3 - 2 = 1     2 - 1 = 1     3 - 1 = 2     3 - 1 = 2

ok nhá

Lời giải chi tiết:

#HT#

1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+2+3

= 6+6+6+6+6+6+6+6+6

= 6x9

= 54

=9x1+9x2+9x3

=9+18+27

=54

Lời giải chi tiết

1²  1                                     1³ 1² – 0²        (0 + 1)²  0²  +1²

2² 1 + 3                                2³ 3² – 1²         (1 + 2)² 1² + 2²

3² 1 + 3 + 5                           3³ 6² – 3²      (2 + 3)²  2² +  3²

                                                     4³ 10² – 6²

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a. 1/3; 1/6; 5/2; 3/2 bạn nha

c

...

Bài 1:

\(\frac14+\frac23=\frac{3}{12}+\frac{8}{12}=\frac{3+8}{12}=\frac{11}{12}\)

\(\frac27+\frac23=\frac{6}{21}+\frac{14}{21}=\frac{6+14}{21}=\frac{20}{21}\)

\(\frac25+\frac13=\frac{6}{15}+\frac{5}{15}=\frac{6+5}{15}=\frac{11}{15}\)

\(\frac23+\frac12=\frac46+\frac36=\frac{4+3}{6}=\frac76\)

\(\frac13+\frac35=\frac{5}{15}+\frac{9}{15}=\frac{5+9}{15}=\frac{14}{15}\)
\(\frac45+\frac13=\frac{12}{15}+\frac{5}{15}=\frac{12+5}{15}=\frac{17}{15}\)

\(\frac18+\frac34=\frac18+\frac68=\frac{1+6}{8}=\frac78\)

\(\frac{1}{36}+\frac{5}{12}=\frac{1}{36}+\frac{15}{36}=\frac{1+15}{36}=\frac{16}{36}=\frac49\)

\(\frac13+\frac16+\frac{1}{18}=\frac{6}{18}+\frac{3}{18}+\frac{1}{18}=\frac{6+3+1}{18}=\frac{10}{18}=\frac59\)

Bài 2:

\(\frac{15}{16}-\frac{3}{16}=\frac{15-3}{16}=\frac{12}{16}=\frac34\)

\(\frac{17}{18}-\frac56=\frac{17}{18}-\frac{15}{18}=\frac{17-15}{18}=\frac{2}{18}=\frac19\)

\(\frac34-\frac49=\frac{27}{36}-\frac{16}{36}=\frac{27-16}{36}=\frac{11}{36}\)

\(\frac12-\frac25=\frac{5}{10}-\frac{4}{10}=\frac{5-4}{10}=\frac{1}{10}\)

\(\frac56-\frac{3}{10}=\frac{25}{30}-\frac{9}{30}=\frac{25-9}{30}=\frac{16}{30}=\frac{8}{15}\)

\(3-\frac13=\frac93-\frac13=\frac{9-1}{3}=\frac83\)

\(\frac45-\frac{1}{10}=\frac{8}{10}-\frac{1}{10}=\frac{7}{10}\)

\(\frac52-1=\frac{5-2}{2}=\frac32\)

\(\frac58-\frac25=\frac{25}{40}-\frac{16}{40}=\frac{25-16}{40}=\frac{9}{40}\)