Question

[Nguyễn Lê Nhật Anh]

So sanh S voi 2 biet: S=1+1/3+1/6+1/10+...+1/45

Answer 1

[Nguyễn Lương Bảo Tiên]

\(S=1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\)

\(\frac{S}{2}=\frac{1}{2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{9\cdot10}\)

\(\frac{S}{2}=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)

\(\frac{S}{2}=1-\frac{1}{10}\)

\(\frac{S}{2}=\frac{9}{10}\)

\(S=\frac{9}{5}