Question

calculati: a) 1+2+3+...+250 b) 2+4+6+...+1000 c) 1+3+5+...+171 d) 8+16+24+...+880

Answer 1

Răspuns:

Explicație pas cu pas:

a) 1 + 2 + 3 +...+ 250 = 250*251/2 = 31375

b) 2 + 4 + 6 +...+ 1000 = 2*(1 + 2 + 3 + ... + 500) = 2*500*501/2 = 500*501

=  250500

c) 1 + 3 + 5 +...+ 171 = 1 + 2 + 3 + 4 + 5 + ... + 171 - (2 + 4 + 6 + ... + 170)

= 171*172/2 - 2*(1 + 2 + 3 + ... + 85) = 171*86 - 2*85*86/2

= 171*86 - 85*86 = 86*(171 - 85) = 86*86 = 7396

d) 8 + 16 + 24 +...+ 880 = 8*(1 + 2 + 3 + ... + 110) = 8*110*111/2 = 4*110*111

= 48840