$\left(51+ 52 + 53 + ... + 100\right)$ = ?
This is an A.P. in which $ a $ = 51, $ l $ = 100 and $ n $ = 50.
$\therefore$Sum =$ \dfrac{n}{2} $$\left( a + l \right)$=$ \dfrac{50}{2} $x (51 + 100) = 25 x 151 = 3775.
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