1² + 2² + 3² + … + 25² = ?
Answer और ExplanationAnswer and explanation
Answer: (B) 5525
12 + 22 + … + n2 = n(n + 1)(2n + 1)6, n = 25
= 25 × 26 × 516
= 25 × 13 × 17 (26 ÷ 2 = 13 और 51 ÷ 3 = 17 करके काटा)
= 25 × 221 = 5525
✓
योग 5525 है।
12 + 22 + … + n2 = n(n + 1)(2n + 1)6, with n = 25
= 25 × 26 × 516
= 25 × 13 × 17 (cancel 26 ÷ 2 = 13 and 51 ÷ 3 = 17)
= 25 × 221 = 5525
✓
The sum is 5525.
SMART APPROACH
25 × 13 × 17: 13 × 17 = 221, और 221 × 25 = 221004 = 5525। इकाई अंक (Unit digit) 5 से सिर्फ़ 5525 और 5555 बचते हैं, और 221 × 25 साफ़ तौर पर 5555 नहीं है।
25 × 13 × 17: 13 × 17 = 221, and 221 × 25 = 221004 = 5525. Unit digit 5 leaves only 5525 and 5555, and 221 × 25 clearly is not 5555.
Source: MTS · 10 Feb 2025 · Shift 1। Solution: Prashant Sir, Vijayastra।Source: MTS · 10 Feb 2025 · Shift 1. Solution by Prashant Sir, from Vijayastra.