+302 Please evaluate\(1/1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+...+2018)\)
+399 \(\frac{1}{\frac{1(1+1)}{2}}+\frac{1}{\frac{2(2+1)}{2}}+\dots + \frac{1}{\frac{2018(2018+1)}{2}}\)
\(\frac{2}{1(2)}+\frac{2}{2(3)}+ \dots+\frac{2}{2018(2019)}\)
\(2(\frac{1}{1(2)}+ \frac{1}{2(3)} + \dots + \frac{1}{2018(2019)})\)
\(\text{Apply } \frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}\)
\(2(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3} +\dots -\frac{1}{2019})\)
\(2(1-\frac{1}{2019})\)
\(\frac{4036}{2019}\)
.+399 \(\frac{1}{\frac{1(1+1)}{2}}+\frac{1}{\frac{2(2+1)}{2}}+\dots + \frac{1}{\frac{2018(2018+1)}{2}}\)
\(\frac{2}{1(2)}+\frac{2}{2(3)}+ \dots+\frac{2}{2018(2019)}\)
\(2(\frac{1}{1(2)}+ \frac{1}{2(3)} + \dots + \frac{1}{2018(2019)})\)
\(\text{Apply } \frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}\)
\(2(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3} +\dots -\frac{1}{2019})\)
\(2(1-\frac{1}{2019})\)
\(\frac{4036}{2019}\)
