Question

Find the sum of ${\sum }_{n=1}^{100}(n-2)$

• A. $-100$
• B. $2250$
• C. $4500$
• D. $4550$
• E. $4850$

Answer 1

Answer: (E)

$4850$

The sum can be computed as follows:

${\sum }_{n=1}^{100}(n-2)={\sum }_{n=1}^{100}n-{\sum }_{n=1}^{100}2$

$=\frac{n(n+1)}{2}-2n$

$=\frac{100(100+1)}{2}-2\left(100\right)$

$=\frac{100\left(101\right)}{2}-200$

$=\frac{10100}{2}-200$

$=5050-200=4850$