This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: The sum is 1 + 2 + + 49 + 50 + 49 + + 3 + 2 + 1. This equals the sum from 1 to 50 plus the sum from 1 to 49: _k=1^50 k + _k=1^49 k Step 2: Use the formula for the sum of the first n natural numbers: _k=1^n k = (n(n+1))/(2) Step 3: Compute _k=1^50 k: (50 × 51)/(2) = (2550)/(2) = 1275 Step 4: Compute _k=1^49 k: (49 × 50)/(2) = (2450)/(2) = 1225 Step 5: Add the results: 1275 + 1225 = 2500 2500