Question

m=1-7+2.8+3.9+...+32.38.
n=1-10+2.11+3 12+...+32-41
Calculaţi n-m:

Answer 1

Răspuns:

n - m = -96

Explicație pas cu pas:

$m = 1 - 7 + 2 - 8 + 3 - 9 + ... + 32 - 38 = \\ = ( - 6) + ( - 6) + ( - 6) + ... + ( - 6) = ( - 6) \cdot 32 = - 192$

$n = 1 - 10 + 2 - 11 + 3 - 12 + ... + 32 - 41 = \\ = ( - 9) + ( - 9) + ( - 9) + ... + ( - 9) = ( - 9) \cdot 32 = - 288$

=>

$n - m = - 288 - ( - 192) = - 288 + 192 = \bf - 96$

Answer 2

$\it m=\underbrace{\it (1-7)+(2-8)+(3-9)+\ ...\ +(32-38)}_{16\ paranteze}=16\cdot(-6)\\ \\ \\ n=\underbrace{\it (1-10)+(2-11)+(3-12)+\ ...\ +(32-41)}_{16\ paranteze}=16\cdot(-9)\\ \\ \\ n-m=16\cdot(-9)-16\cdot(-6)=16(-9+6)=16\cdot(-3)=-48$