Sequences & Series QuestionWatch
note that it is no calculator.
So here's my working so far, but can someone give me a hint? Am I supposed to just work out r numerically? surely not - the answer is r = 3 but how am I supposed to get it?
11th degree polynomials are extremely difficult to solve, and this one isn't so nice. Are you absolutely certain you can't use a calculator for this question, and that the non-calc icon could be a misprint?
2 922 920 which has 7 digits
Divide by 11, the sum (r^12-1)/(r-1) has 6 digits. Note the first 12 terms goes up to r^11.
So r^2 ~ 10, so r~3.
Assuming integers, 3 is likely to be the solution and its possible to check by repeated multiplication by 9 up to 9^6 or by dividing the original by 11, multiplying by 2 and adding 1, then using the divisibility test for 3 or 9.