Question

If the set of natural numbers is partitioned into subsets `S_1={1},S_2={2,3},S_3={4,5,6}` and so on then find the sum of the terms in `S_(50)dot`

Answer 1

The number of terms in the groups are `1,2,3,"...."`
`therefore` The number of terms in the 50th group =50
`therefore` The last term of 1st group = 1
The last term of 2nd group `=3=1+2`
The last term of 3rd group `=6=1+2+3`
`vdots " "vdots " "vdots " "vdots " "vdots " "vdots`
The last term of 49th group `=+2+3+"......" + 49`
`therefore` First term of 50th group `=1+(1+2+3+"..."+ 49)`
`=1+(49)/(2)(1+49)=1226`
`therefore S_(50_=(50)/(2){2xx1226+(50-1)xx1}`
`=25xx2501=62525`