Question

Calculati: (1+2+3+4...+99+100)-(1+2+3+4...+99)

Answer 1

(1+2+3+4..+99+100)-(1+2+3+4...+99)=100

Answer 2

$\displaystyle (1+2+3+4...+99+100)-(1+2+3+4...+99)= \\ \\ = \frac{100(100+1)}{2} - \frac{99(99+1)}{2} = \frac{100 \times 101}{2} - \frac{99 \times 100}{2} = \\ \\ = \frac{10100}{2} - \frac{9900}{2} =5050-4950=100$