IIT JEE , AIEEE Forum - Mathematics , Algebra

sunip_the_mini_mastermind

Q.   If the set of natural numbers is partitioned into subsets such that

      S₁ ={1} , S₂ ={2,3}, S₃ ={4,5,6} , S₄ ={7,8,9,10} .........

       then find the sum of members in S₅₀ .

gcch29

first term of 50 group
series of first term of each group
1,2,4,7...............
1st order difference 2-1 , 4-2 ,7-4..........
1, 2,3.......

2nd order difference 1,1..........

so general term =an^2 +b.n +c
a+b+c =1 for 1st general term n=1
4a+2b+c=2 for 2nd general term n=2
9a+3b+c=4 for 3rd general term n=3

on solving we get
a= 1/2
b= -1/2
c=1
tn= (n^2 -n)/2 +1
t(50) =1226
no of terms in 50th group =50
sum =50/2 * [2*1226 + (50-1) *1]
=25[2452+49]
=25 *2501
=62525
sum of nth row
first term =1/2(n^2 -n +2)
n=n
d=1
Sn = n(n^2 +1)/2

krishna.gopal

Perfect answer gcch29. Well done

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