Question

In urma efectuarii calculului 1-2+3-4+5-6+...+99-100+50 se obtine:
a. 0
b. -50
c. -1
d. 1

Repede va rog!

Answer 1

Răspuns:

1-2+3-4+5-6+...+99-100+50=

=(1+3+5+...+99) - (2+4+6+...+100)+50

1 = 0×2 +1

3 = 1×2 +1

5 = 2×2 +1

.....

99 = 49×2 +1

2 = 0×2 +2

4 = 1×2 +2

6 = 2×2 +2

....

100 = 49×2 +2

=2(1+2+3+..+49) + 50 - (2(1+2+3+..+49) + 2×50 ) +50

= 2(1+2+3+..+49) +50 -2(1+2+3+..+49) -2×50 +50

=50 -2×50 +50

= 0