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Answer 1 · 2017-09-21T07:51:01

#0.878787...=> 87/100 + 87/10000 + 87/1000000 +...#

Hence, 1st term #a = 87/100# and common ratio #r = 1/100#

Now, #S_oo = a/(1 - r)#

i.e. #a/(1 - 1/100) = (100a)/99#

So, with #a = 87/100# we have:

#(100/99)(87/100) = 87/99#

or, #29/33#

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