The student's error is that the common ratio would not be equal to 3/2.
What is Common Ratio:
The general form of representing a geometric progression is a1, (a1r), (a1r2), (a1r3), (a1r4) ,... where a1 is the first term of GP, a1r is the second term of GP, and r is the common ratio.
Common Ratio Formula:
Common ratio,
r =a n / a n−1
where,
an is the nth term of the geometric progression.
an−1 is the (n - 1)t h term of the geometric progression.
Now,
[tex]S_{infinity} = 2a_{1} \\\\= a_{1} / 1-r\\\\2a_{1} = a_{1} / 1-r\\\\= 1-r = 1/ 2\\\\r = 1/2 - 1\\\\r = 1/2[/tex]
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