\(A=\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{36\times37\times38}+\frac{1}{37\times38\times39}\)

\(2A=\frac{2}{1\times2\times3}+\frac{2}{2\times3\times4}+\frac{2}{3\times4\times5}+...+\frac{2}{36\times37\times38}+\frac{2}{37\times38\times39}\)

\(2A=\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+...+\frac{1}{37\times38}-\frac{1}{38\times39}\)

\(2A=\frac{1}{1\times2}-\frac{1}{38\times39}\)

\(2A=\frac{741}{1482}-\frac{1}{1482}\)

\(2A=\frac{370}{741}\)

\(A=\frac{370}{741}:2=\frac{185}{741}\)

2/1×2×3 + 2/2×3×4 + 2/3×4×5 + ... + 2/36×37×38 + 2/37×38×39

= 1/1×2 - 1/2×3 + 1/2×3 - 1/3×4 + 1/3×4 - 1/4×5 + ... + 1/36×37 - 1/37×38 + 1/37×38 - 1/38×39

= 1/1×2 - 1/38×39

= 1/2 - 1/1482

= 370/741

\(\text{Ta có: }\) \(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}+....+\frac{1}{37.38}-\frac{1}{38.39}\)

                  \(=\frac{1}{2}-\frac{1}{38.39}\)

                  \(=\frac{1}{2}-\frac{1}{1482}\)

                  \(=\frac{370}{741}\)

A=\(\frac{1}{1x2x3}+\frac{1}{2x3x4}+...+\frac{1}{37x38x39}\)

=\(\frac{1}{2}x\left(\frac{1}{1x2}-\frac{1}{2x3}+\frac{1}{2x3}-\frac{1}{3x4}+...+\frac{1}{37x38}-\frac{1}{38x39}\right)=\frac{1}{2}x\left(\frac{1}{2}-\frac{1}{38x39}\right)=\frac{185}{741}\)

gcjjjjjjjjjjjhm.f

Vũ Thị Trang lại là một nạn nhân tiếp tục bị báo cáo

\(=\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+...+\frac{1}{37\times38}-\frac{1}{38\times39}\)

\(=\frac{1}{1\times2}-\frac{1}{38\times39}=\frac{1}{2}-\frac{1}{1482}=\frac{370}{741}\)

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{36.37.37}\)

\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{36.37.38}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{36.37}-\frac{1}{37.38}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{37.38}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{1406}\right)\)

\(=\frac{1}{2}.\frac{351}{703}\)

\(=\frac{351}{1046}\)

\(\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....-\frac{1}{36}+\frac{1}{37}-\frac{1}{38}+\frac{1}{38}-\frac{1}{39}\)

=\(\frac{1}{1}-\frac{1}{39}\)

=\(\frac{38}{39}\)

đảm bảo đúng

A = 2/1x2x3 + 2/2x3x4 + 2/3x4x5 + ... + 2/36x37x38 + 2/37x38x39

A = 1/1x2 - 1/2x3 + 1/2x3 - 1/3x4 + 1/3x4 - 1/4x5 + ...+ 1/36x37 - 1/37x38 + 1/37x38 - 1/38x39

A = 1/2 - 1/38x39

A = 370/741

Tớ ko chắc là đúng đâu

bài 

Nguyễn Hà Thương sai chưa chia 2

\(A=\frac{370}{741}\)

A=\(\frac{370}{741}\)

A = \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\)

= \(\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{37.38.39}\right)\)

= \(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\right)\)

= \(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{38.39}\right)\)

= \(\frac{1}{2}\left(\frac{1}{2}-\frac{1}{1482}\right)\)

= \(\frac{1}{2}.\frac{390}{781}=\frac{195}{781}\)

=195/781

= 40 / 39