Question

Dau Coroana !! Plssss​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

2 + 4 + 6 + 8 + ... + 100 = 2*(1 + 2 + 3 + 4 + ... + 50) = 2*50*51/2 = 50*51 = 2550

b)

1 + 4 + 7 + 10 + ... + 91 = 1 + (3 + 1) + (3*2 + 1) + (3*3 + 1) + ... + (3*30 + 1)

= 1 + (3 + 3*2 + 3*3 + ... + 3*30) + 1*30

= 1 + 3*(1 + 2 + 3 + ... + 30) + 30

= 1 + 3*30*31/2 + 30

= 1 + 1395 + 30

= 1426

c)

S = 1 + 2^1 + 2^2 + 2^3 + ... + 2^19

2S = 2^1 + 2^2 + 2^3 + 2^4 + ... + 2^20

2S - S = 2^1 + 2^2 + 2^3 + 2^4 + ... + 2^20 - (1 + 2^1 + 2^2 + 2^3 + ... + 2^19)

S = 2^1 + 2^2 + 2^3 + 2^4 + ... + 2^20 - 1 - 2^1 - 2^2 - 2^3 - ... - 2^19

S = 2^20 - 1