Question

Tính giá trị các biểu thức sau:

\(B=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{190}\)

Answer 1

\(B=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{190}\)

=\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{380}\)

=\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{19.20}\)

=\(2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\right)\)

=\(2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\right)\)

=\(2.\left(\frac{1}{2}-\frac{1}{20}\right)\)

=\(2.\frac{9}{20}\)=\(\frac{9}{10}\)