Question

Efectuați: ( 2+4+6+...+400) : (4+8+12+...+100)​

Answer 1

$2 + 4 + 6 + ... + 400 = \\ 2 \times (1 + 2 + 3 + ...200) = \\ 2 \times \frac{200 \times 201}{2} = \\ = 200 \times 201$

$4 + 8 + 12 + ... + 100 = \\ 4 \times (1 + 2 + 3 + ... + 25) = \\ 4 \times \frac{25 \times 26}{2} = \\ = 2 \times 25 \times 26$

$(2 + 4 + 6 + ... + 400) \div (4 + 8 + 12 + ... + 100) = \\ \frac{200 \times 201}{2 \times 25 \times 26} = \frac{4 \times 201}{26} = \frac{2 \times 201}{13} = \frac{402}{13}$

Answer 2

Răspuns:

( 2+4+6+...+400) : (4+8+12+...+100)​=

2(1+2+3+..+200):4(1+2+3+...+25)=

2·[200·(200+1)]/2:4·[25·(25+1)]/2=

40200:1300=30,92

cred ca ai omis ceva in ex