Question

Buna! Ma poate ajuta cineva??
a |-1|+|-2|+|-3|+......+|-50|
b |-3|+|-6|+|-9|+......+|-90|
c |+2|+|+5|+......+|+29|
d |-2|¹+|-2|²+......+|-2|²⁰​

Answer 1

Răspuns:

a)|-1|=1 ;|-2|=2....|-50|=50 => |-1|+|-2|+|-3|+......+|-50|=1+2+3+..50= 50•51/2=25•51=1275

b) |-3|=3 |-6|=6......|-90|=90 => |-3|+|-6|+|-9|+......+|-90|=3+6+9....+90=3(1+2+3+....30)= 3• 30•31/2=3•15•31=1395

La c) nu am inteles ...merg din 3 in 3?

d) | -2|=2 =>

|-2|¹+|-2|²+......+|-2|²⁰=2¹+2²+2³+....2²⁰=2• 2²⁰-1=2²¹-1

Explicație pas cu pas:

1+2+3+....n=n(n+1)/2

Answer 2

Răspuns:

Explicație pas cu pas:

a |-1|+|-2|+|-3|+......+|-50|

1 + 2 + 3 + ...+ 50 = 50*(1 + 50)/2 = 50*51/2 = 25*51 = 1275

_____________

b |-3|+|-6|+|-9|+......+|-90|

3 + 6 + 9 + ...+ 90 = 30*(3 + 90)/2 = 30*93/2 = 15*93 = 1395

______________

c |+2|+|+5|+......+|+29|

2 + 5 + ....+ 29 = 10*(2 + 29)/2 = 10*31/2 = 5*31 = 155

______________

d

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

2S = 2^2 + 2^3 + ....+ 2^21

2S - S = S = 2^2 + 2^3 + ....+ 2^21 - 2^1 - 2^2 - 2^3 - ....- 2^20

= 2^21 - 2