Problem 39
Question
Find \(1+2+3+4+\cdots+100,\) the sum of the first 100 natural numbers.
Step-by-Step Solution
Verified Answer
The sum of the first 100 natural numbers is 5050.
1Step 1: Identify the characteristics of the arithmetic series
The first term \(a\) is 1 and the last term \(l\) is 100.
2Step 2: Apply the formula for the sum of an arithmetic series
The formula for the sum of the first \(n\) terms of an arithmetic sequence is \(S_n = n/2 (a + l)\). In this case: \(S_{100} = 100/2 (1 + 100)\)
3Step 3: Simplify the expression
Solving the expression: \(S_{100} = 50(101) = 5050\)
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