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English: A plot showing how the ratio test test is proven in the convergent case. Given a sequence like the blue one, for which the ratio of adjacent terms | a n + 1 / a n | {\displaystyle |a_{n+1}/a_{n}|} converges to L < 1, we identify a ratio r = (L+1)/2 and show that for large enough n the sequence is dominated by the simple geometric ...
For example, a ratio of 3:2 is the same as 12:8. It is usual either to reduce terms to the lowest common denominator, or to express them in parts per hundred . If a mixture contains substances A, B, C and D in the ratio 5:9:4:2 then there are 5 parts of A for every 9 parts of B, 4 parts of C and 2 parts of D.
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