Solve 5(x-1)^1/3 = 20
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The infinite sequence of geometric terms is divergent if you try to add up all the terms. Sure the first 20 terms will add up to a fixed number but this isn't true for an infinite number of terms. The reason why the infinite series diverges is because r = 1.1 is larger than 1. If r > 1 then the infinite series diverges. It only converges if -1 < r < 1.
To write this in sigma notation, you would write
which is the result of adding the terms of 100(1.1)^(n-1) for n = 1 all the way up to n = 20. You can compute this by hand or preferably with a calculator or spreadsheet program
To write this in sigma notation, you would write