SOLUTION: Find the sum of the first 20 terms of the series 1+3+9+27... Please explain with a formula. Thank you!

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Question 472498: Find the sum of the first 20 terms of the series
1+3+9+27...
Please explain with a formula. Thank you!
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
I will show you the formula plus how it is derived so that you don't blindly memorize it. Blindly memorizing formulas is a common pitfall students make, and it makes students less likely to actually "understand" the material.

Let



Then,



We can do 3S - S and obtain lots of cancellation:





To generalize, you would let the common difference be something like "r" then the denominator of 2 would be replaced with r-1. Also, for an arbitrary exponent n (here n = 19) the 20 would be replaced with n+1.