Question

5+10+15+20+...+2010-9-13-17-...-1709 va rooooogg!!! ​

Answer 1

Răspuns:

Explicație pas cu pas:

5+10+15+20+...+2010-9-13-17-...-1709 =

5·(1+2+3+....+402) - (9+13+17+....1709) = A - B

A = 5·(1+2+3+....+402) = 5·(1+402)·402:2 = 5·403·201 = 405015

B = (9+13+17+....1709)  = (9+1709)·[(1709-9):4+1]:2 = 859·426 =>

B = 365934

A-B = 405015-365934 = 39081

Answer 2

5+10+15+20+...+2010-9-13-17-21-...-1709 =

= 5·(1+2+3+4+...+402) - (4·1+5) - (4·2+5) - (4·3+5) - ... - (4·426+5) =

= 5·(402·403)/2 - 4·(1+2+3+...+426) - 5·426 =

= 5·201·403 - 4·(426·427)/2 - 2130 =

= 405015 - 2·181902 - 2130 =

= 39081