Question

Tính A/B biết:

A = 1/2 + 1/3 + 1/4 + ... + 1/200

B = 1/199 + 2/198 + 3/197 + ... + 199/1

Answer 1

Ta có:

\(B=\frac{1}{199}+\frac{2}{198}+\frac{3}{192}+...+\frac{198}{2}+199.\)

Bây giờ tách cái 199 ở cuối ra rồi làm như sau

\(=\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+...+\left(\frac{197}{3}+1\right)+\left(\frac{198}{2}+1\right)+1\)

\(=\frac{200}{199}+\frac{200}{198}+...+\frac{200}{3}+\frac{200}{2}+\frac{200}{200}\)

\(=200\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{199}+\frac{1}{200}\right)\)

= 200 A

Vì B =200xA nên A/B = 1/200