Question

Dau coroana!!!!!!!!!

Answer 1

a)
 s=1+2+2^2+2^3+2^4+...................+2^99
2s=2+2^2+2^3+2^4+2^5+...............+2^100
2s-s=s=2^100 - 1

b)
s=1+3+3^2+3^3+............................+3^999
3s=3+3^2+3^3+3^4+......................+3^1000
3s-s=2s=3^1000 - 1
s=(3^1000 - 1)/2

c)
s=1+a+a^2+a^3+............................+a^100
as=a+a^2+a^3+a^4+.......................+a^101
as-s=s(a-1)=a^101 - 1
s=(a^101 - 1)/(a-1)

d)
s=1-2+2^2-2^3+2^4-.....................-2^11+2^12
2s=2-2^2+2^3-2^4+2^5-...............-2^12+2^13
2s+s=3s=2^13 + 1
s=(2^13 + 1)/3

e)
s=1/2-1/2^2+1/2^3-1/2^4+................+1/2^15-1/2^16
s/2=1/2^2-1/2^3+1/2^4-1/2^5+..........+1/2^16-1/2^17
s+s/2=1/2 - 1/2^17
s=2(1/2-1/2^17)/3
s=(1-1/2^16)/3