Kabir knows the sum of the first n odd numbers always equals n² (like 1+3+5=9=3²)

Why

Kabir has correctly learned a genuinely beautiful pattern — odd numbers really do build up to perfect squares this way, and noticing that a nice pattern might extend further is exactly the right instinct for exploring maths. The trouble is assuming a pattern must transfer just because it worked somewhere similar-looking, without actually testing the new case. Try it with n=3: the first 3 even numbers are 2, 4, 6, and their sum is 2+4+6=12. But 3² is 9, and 12 does not equal 9 — the pattern breaks immediately. The real pattern for even numbers is different: the sum of the first n even numbers is n×(n+1), which for n=3 gives 3×4=12, matching what was actually computed. Odd numbers build squares because each new odd number added is exactly the right size to complete the next square shape; even numbers, added the same way, build a slightly different, rectangular shape instead. Test: try n=4 both ways — first 4 odd numbers 1+3+5+7=16=4² (matches); first 4 even numbers 2+4+6+8=20, while 4²=16 (doesn't match, but 4×5=20 does). No, the sum for even numbers comes out different: it follows its own pattern, n×(n+1), and a pattern proven for odd numbers cannot simply be assumed to carry over to a different set of numbers without checking.