Use the formula for the sum of a geometric series to find the sum, or state that the series diverges. frac{25}{9}+frac{5}{3}+1+frac{3}{5}+frac{9}{25}+frac{27}{125}+...

Albarellak

Albarellak

Answered question

2021-03-09

Use the formula for the sum of a geometric series to find the sum, or state that the series diverges.
259+53+1+35+925+27125+

Answer & Explanation

2k1enyvp

2k1enyvp

Skilled2021-03-10Added 94 answers

The given geometric series is,
259+53+1+35+925+27125+
The first term is, a1=259
Determine the common ratio.
d=a2a1
=(53)(259)
=(53)(925)
=35
Since r<1,
The sum of the geometric series is,
Sn=a(1rn)1r
Substitute the values.
Sn=(259)(1(35)n)1(35)
=(259)(5n3n5n)(535)
Sn=(259)(5n3n5n)(52)
Sn=(5318)(5n3n5n)
=(118)(5n3n5n3)
Sum of the series to infinite terms is,
S=a1r
=(259)1(35)
=(259)(535)
=(259)(52)
=12518

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