Question

Pa ma đâu òi, giúp cn với TT

\(\frac{1}{1+2}+\frac{1}{1+2+3}+....+\frac{1}{1+2+3+.....+2014}\) 

có giá trị = ? 

Answer 1

ĐẶt A = \(\frac{1}{1+2}+\frac{1}{1+2+3}+....+\frac{1}{1+2+3+....+2014}\)

\(\frac{1}{2}A=\frac{1}{2.3}+\frac{1}{3.4}+........+\frac{1}{2014.2015}\)

\(\frac{1}{2}A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-.....-\frac{1}{2014}+\frac{1}{2014}-\frac{1}{2015}\)

\(\frac{1}{2}A=\frac{1}{2}-\frac{1}{2015}=\frac{2013}{4030}\)

A = 2013/4030 : 1/2 = 2013/2015