SOLUTION: Find the remainder when (x^9 + 2x^8 + 3x^7 +…+ 9^x) is divided by (x – 1). A. 45 C. 180 B. 90 D. 360

Algebra ->  Sequences-and-series -> SOLUTION: Find the remainder when (x^9 + 2x^8 + 3x^7 +…+ 9^x) is divided by (x – 1). A. 45 C. 180 B. 90 D. 360      Log On


   

Question 982382: Find the remainder when (x^9 + 2x^8 + 3x^7 +…+ 9^x) is divided by (x – 1).
A. 45 C. 180
B. 90 D. 360
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The polynomial you meant to write is P%28x%29=x%5E9+%2B+2x%5E8+%2B+3x%5E7+%2B%22...%22%2B8x%5E2%2B9x ,
where for each term the power of x and the coefficient add to 10 .
The remainder when a polynomial P%28x%29 is divided by %28x-1%29 is P%281%29 .
In this case P%281%29=1%2B2%2B3%2B%22...%22%2B8%2B9=highlight%2845%29
I could add using pencil and paper, or a calculator,
but I know that sum to be the sum of red%289%29 consecutive terms of an arithmetic sequence,
with the first and last of those terms being 1 and green%289%29 .
So, .