Câu a:

S = 1.3 + 3.5 + 5.7 + ...+ 41.43

6S = 1.3.6 + 3.5.6 + ...+ 41.43.6

1.3.6 = 1.3.(5 + 1) = 1.3.5 + 1.3.1

3.5.6 = 3.5(7 - 1) = 3.5.7 - 1.3.5

5.7.6 = 5.7.(9 - 3) = 5.7.9 - 3.5.7

................................................................

41.43.6 = 41.43.(45 - 39) = 41.43.45 - 39.43.45

Cộng vế với vế ta có:

6S = 1.3.1 + 41.43.45

6S = 3 + 1763.45

6S = 3+ 79335

6S = 79338

S = 79338 : 6

S = 13223

Ta có: \(\frac{2}{1\times3}+\frac{2}{3\times5}+\cdots+\frac{2}{41\times43}\)

\(=1-\frac13+\frac13-\frac15+\cdots+\frac{1}{41}-\frac{1}{43}\)

\(=1-\frac{1}{43}=\frac{42}{43}\)

Đặt A =2/1x3+2\3x5+................+2/41x43

A =1/1-1/3+1/3-1/5+...................+1/41-1/43

A=1-1/43

A=42/43 

A=2/1X3+2/3X5+2/5X7+. . .+2/41X43

A=1/1-1/3+1/3-1/5+1/5-1/7+. . .+1/41-1/43

A=1/1-1/43

A=42/43

Tick mk nhé

Bấm vào câu hỏi tương tự : 

A = 1 x 3 + 5 x 7 + 9 x 11 + ... + 99 x 101
6A = 6 x (1 x 3 + 5 x 7 + 9 x 11 + ... + 99 x 101)
6A = 1 x 3 x 6 + 5 x 7 x 6 + 9 x 11 x 6 + ... + 99 x 101 x 6
6A = 1 x 3 x (5 + 1) + 3 x 5 x (7 - 1) + 5 x 7 x (9 - 3) + ⋯ + 99 x 101 x (103 - 97)
6A = 1 x 3 x 1 + 1 x 3 x 5 + 3 x 5 x 7 - 1 x 3 x 5 + 5 x 7 x 9 - 3 x 5 x 7 + ⋯ + 99 x 101 x 103 - 97 x 99 x 101
6A = 1 x 3 x 1 + (1 x 3 x 5) + (3 x 5 x 7) - (1 x 3 x 5) + (5 x 7 x 9 ) - (3 x 5 x 7) + ⋯ + (99 x 101 x 103) - (97 x 99 x 101)
6A = 3 - 99 x 101 x 103 = 1019703
=> A = 1019703/6

Ta có:

A = \(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{7x9}+\frac{2}{9x11}\)

= \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

= \(\frac{1}{1}-\frac{1}{11}\)

=\(\frac{10}{11}\)

TOÁN LỚP 4 HẢ

A = 1 x 3 + 5 x 7 + 9 x 11 + ... + 99 x 101
6A = 6 x (1 x 3 + 5 x 7 + 9 x 11 + ... + 99 x 101)
6A = 1 x 3 x 6 + 5 x 7 x 6 + 9 x 11 x 6 + ... + 99 x 101 x 6
6A = 1 x 3 x (5 + 1) + 3 x 5 x (7 - 1) + 5 x 7 x (9 - 3) + ⋯ + 99 x 101 x (103 - 97)
6A = 1 x 3 x 1 + 1 x 3 x 5 + 3 x 5 x 7 - 1 x 3 x 5 + 5 x 7 x 9 - 3 x 5 x 7 + ⋯ + 99 x 101 x 103 - 97 x 99 x 101
6A = 1 x 3 x 1 + (1 x 3 x 5) + (3 x 5 x 7) - (1 x 3 x 5) + (5 x 7 x 9 ) - (3 x 5 x 7) + ⋯ + (99 x 101 x 103) - (97 x 99 x 101)
6A = 3 - 99 x 101 x 103 = 1019703
=> A = 1019703/6

\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.........+\frac{1}{13}-\frac{1}{15}\)

\(=1-\frac{1}{15}\)

\(=\frac{14}{15}\)