a) 15 + 16 + ... + 95 =
= (1+2+3+...+95) - (1+2+3+...+14) =
= (95•96)/2 - (14•15)/2 =
= 95•48 - 7•15 =
= 4455
b) 49 + 50 + 51 + ... + 250 =
= (1+2+3+...+250) - (1+2+3+...+48) =
= (250•251)/2 - (48•49)/2 =
= 125•251 - 24•49 =
= 30199
c) 24 + 26 + 28 + ... + 100 =
= (2+4+6+...+100) - (2+4+6+...+24) =
= 2•(1+2+3+...+50) - 2•(1+2+4+...+12) =
= 2•(50•51)/2 - 2•(12•13)/2 =
= 50•51 - 12•13 =
= 2394
d) 20 + 25 + 30 + ... + 300 =
= 5•(4+5+6+...+60) =
= 5•[(1+2+3+...+60) - (1+2+3)] =
= 5•(60•61)/2 - 5•6 =
= 5•30•51 - 30 =
= 4620
e) 19 + 21 + 23 + ... + 2019 =
= (1+3+5+...+2019) - (1+3+5+...+17) =
= [(2019+1)/2]² - [(17+1)/2]² =
= 1008² - 9² =
= 1015983
