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horsena [70]
2 years ago
14

Given that the following two geometric series(meetkundige reekse) are covergent 1+x+x²+x³+... And 1-x+x²-x³+... Determine the va

lue(s) of x for witch the sum of the following two series is equel​
Mathematics
1 answer:
Oksanka [162]2 years ago
3 0

The sets are (1,-1) or (-1,1)

Lets see

Take until 4terms

#1

\\ \rm\longmapsto S_4=1+1+1^2+1^3=1+1+1+1=4(1,-1)

\\ \rm\longmapsto S_4=1+(-1)+(-1)^2+(-1)^3=1-1+1-1=0(-1,1)

#2

\\ \rm\longmapsto S_4=1-(-1)+(-1)^2-(-1)^3=1+1+1+1=4(1,-1)

\\ \rm\longmapsto S_4=1-1+(1)^2-1^3=1-1+1-1=0(-1,1)

Hence verified

Another set can be (0,0)

Proof:-

\\ \ast\rm\longmapsto S_3=1+0+0^2=1

\\ \ast\rm\longmapsto S_3=1-0+0^2=1

Hence verified.

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