Answer
Conjecture is correct.
Work Step by Step
1+2+3+4+5+6 = $\frac{6 *7}{2}$
L.H.S = 1+2+3+4+5+6
= 21
R.H.S= $\frac{6 *7}{2}$ = $\frac{42}{2}$ = 21
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