Please evaluate1/1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+...+2018)
11(1+1)2+12(2+1)2+⋯+12018(2018+1)2
21(2)+22(3)+⋯+22018(2019)
2(11(2)+12(3)+⋯+12018(2019))
Apply 1n(n+1)=1n−1n+1
2(11−12+12−13+⋯−12019)
2(1−12019)
40362019
.11(1+1)2+12(2+1)2+⋯+12018(2018+1)2
21(2)+22(3)+⋯+22018(2019)
2(11(2)+12(3)+⋯+12018(2019))
Apply 1n(n+1)=1n−1n+1
2(11−12+12−13+⋯−12019)
2(1−12019)
40362019