Question

If N the set of natural numbers is partitioned into groups S₁ ={1} , S₂ = {2,3}, S₃ = {4,5,6},...., find the sum of the numbers in S₅₀

Answer 1

s1=(1) s2(2,3), s3(4,5)................

we have to find sum of set s50( ) ??

Look each set carefully numbers seems to be like 1,2,3,4,5,6,7,8,9,10,..............

hence s50 set contain 50 element

and s49 contain 49 element

then sum of 1st 49 terms 1+2+3+4+5+6+7+8+9+10,..............48+49

n(n+1)/2 =49(49+1)/2=1225

that means last element of s49 is 1225.


hence first element of s50 is start from 1226

and last element is 1225+50=1275.

so the element in the s50(1226,1227,1228.............1275)

so sum= n/2(2a+(n-1)d) by airthemetic mean formula

put the value

=> 50/2(2*1226+(50-1)1)

=>625625