E-GP02 · Recover both ratio signs from two sums
A GP has sum to infinity 54 and sum of its first two terms 48.
Show that \(\displaystyle r^{2}= \frac{1}{9}\).
Find every possible pair \((a,r)\) and check convergence.
For the positive-ratio solution, find the least n for which the omitted sum is strictly less than \(\displaystyle \frac{1}{10}\).
Complete-answer checking, worked solutions and indicative written criteria.
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