evaluate 1+2x3+3x9+...+9+38: what does '...' mean?

Hello, nowayitsmel!

\(\displaystyle \text{Evaluate: }\;1 + 2\cdot3 + 3\cdot9 + 4\cdot27 + \hdots + 9\cdot3^8\)

The 'three dots' mean: "and so on in the same manner".

\(\displaystyle \text{We have: }\;S \;=\;1\cdot3^0 + 2\cdot3^1 + 3\cdot3^2 + 4\cdot3^3 + 5\cdot3^4 + 6\cdot3^5 + 7\cdot3^6 + 8\cdot3^7 + 9\cdot3^8\)


I suppose they expect us to find the sum by some algebraic method.
. . I did . . . and it's much easier to do the arithmetic.

 
Top