1+2+3+……+49+50+49+48+….+3+2+1) fdlds cjkcj gS&

Mathematics

ScanSolve AI Answer

Answer

2500

Step 1: The sum is 1+2++49+50+49++3+2+11 + 2 + \dots + 49 + 50 + 49 + \dots + 3 + 2 + 1.
This equals the sum from 1 to 50 plus the sum from 1 to 49:
k=150k+k=149k\sum_{k=1}^{50} k + \sum_{k=1}^{49} k

Step 2: Use the formula for the sum of the first nn natural numbers:
k=1nk=n(n+1)2\sum_{k=1}^{n} k = \frac{n(n+1)}{2}

Step 3: Compute k=150k\sum_{k=1}^{50} k:
50×512=25502=1275\frac{50 \times 51}{2} = \frac{2550}{2} = 1275

Step 4: Compute k=149k\sum_{k=1}^{49} k:
49×502=24502=1225\frac{49 \times 50}{2} = \frac{2450}{2} = 1225

Step 5: Add the results:
1275+1225=25001275 + 1225 = 2500

2500

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Quick Answer

The sum is 1 + 2 + + 49 + 50 + 49 + + 3 + 2 + 1.

1+2+3+……+49+50+49+48+….+3+2+1) fdlds cjkcj gS&
Mathematics

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