Determine whether the geometric series is convergent or divergent. 10-4+1.6-0.64+.... If it's

Priscilla Johnston 2021-12-10 Answered
Determine whether the geometric series is convergent or divergent.
104+1.60.64+.
If it's convergent find its sum.
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Expert Answer

Juan Spiller
Answered 2021-12-11 Author has 38 answers

Step 1
Let S=104+1.60.64+
Given that S is a geometric series,
The known fact is that a geometric series a+ar+ar2+ is convergent |r|<1.
By comparing the given series with its general form,
a=10, r=410=0.4.
|r|=|0.4|<1.
This implies that the series 104+1.60.64+ is convergent.
Step 2
The known fact is that a geometric series a+ar+ar2+ - is equal to a1r(r<1).
104+1.60.64±=(10+1.6+0.256+)(4+0.64+)
=(1010.16)(410.16)[a=10,r=0.16 in first geometric seriesa=4,r=0,16in second geometric series]
=(10410.16)
=(60.84)
=7.1428571428571429

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