Question

Calculează:
a) 1+2+...+50)+(1+2+3+...+200)
c) 2+4+6+...+100​

Answer 1

a)

$1 + 2 + 3 + ... + 50 + 1 + 2 + 3 + ... + 200 = \\ \\ \frac{50 \times (50 +1)}{2} + \frac{200 \times (200 + 1)}{2} = \\ \\ 25 \times 50 + 100 \times 201 = \\ 1275 + 20100 = \\ 21375$

b)

$2 + 4 + 6 + ... + 100 = \\ 2( 1 + 2 + 3 + .. + 50) = \\ \\ 2 \times \frac{50 \times (50 + 1)}{2} = \\ \\ 50 \times 51 = \\ 2550$