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08 Jan 2021, 06:01
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Consider the sets of consecutive integers {1}, {2, 3}, {4, 5, 6}, {7, 8, 9, 10}, ..., where each set contains one more element than the preceding one, and where the first element of each set is one more than the last element of the preceding set. Let \(S_n\) be the sum of the elements in the \(n_{th}\) set. What is the value of \(S_{50}\)?
(A) 42,455
(B) 61,250
(C) 62,525
(D) 65,525
(E) None of these
Are You Up For the Challenge: 700 Level Questions
(A) 42,455
(B) 61,250
(C) 62,525
(D) 65,525
(E) None of these
Are You Up For the Challenge: 700 Level Questions
N, the set of natural numbers is portioned into subsets
S1={1}
S2={2,3}
S3={4,5,6}
S4={7,8,9,10} and so on.
The sum of the numbers in subset S50 is
(A) 61,250
(B) 65,525
(C) 42,455
(D) 62,525
(E) None of these
S1={1}
S2={2,3}
S3={4,5,6}
S4={7,8,9,10} and so on.
The sum of the numbers in subset S50 is
(A) 61,250
(B) 65,525
(C) 42,455
(D) 62,525
(E) None of these
08 Jan 2021, 07:16
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Bunuel
So \(1^{st}\) set has 1 element, while the \(2^{nd}\) has 2 elements and so on.
Thus the \(50^{th}\) set will have 50 elements.
Let us check on the largest digit in each set now.
\(1^{st}\) set has 1, while the \(2^{nd}\) has 3 and \(3^{rd}\) has 6 and so on.
What is the connection between (1 and 1); (2 and 3) and (3 and 6).
The second digit is the SUM of the positive integers till the first integer => (n and Sum of first n positive integers)
So, in the 50th set, it will be 'Sum of first n positive integers'=\(\frac{50*51}{2}=1275\) =>(50 and 1275)
So 50th set has 50 elements and the largest is 1275...{a,.....,1275} => a=1275-50+1=1226
{1226,1227,....1274,1275}
\(S_{50}=1226+1227+....1274+1275=\frac{1226+1275}{2}*50=62,525\)
C
02 May 2025, 06:10
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