An infinite geometric series has 1 and 1⁄5 as its first two terms: 1, 1⁄5, 1⁄25, 1⁄125, . . . . What is the sum, S, of the infinite series?

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Answer 1 · 2016-04-17T11:24:00

#s=5/4#

Put #s=1+1/5+1/25+1/125....#

If we divide by 5 we obtain:

#s/5=1/5+1/25+1/125....#

Add 1:

#1+s/5=1+1/5+1/25+1/125...#, but this is equal to #s#

So, we obtain:

#1+s/5=s#

#5+s=5s#

#5=4s#

#s=5/4#