Question

Tính tổng:

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

Answer 1

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

<=> 2B = \(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+....+\frac{2}{37.38.39}\)

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

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

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

Answer 2

= kho qua minh khong bit ?.............................