Question 1158775: Find the sum.
1 + 4 + 16 + · · · + 65,536
Answer by ikleyn(52795)   (Show Source):
You can put this solution on YOUR website! .
Use the formula for the sum of a geometric progression.
If  ,  ,  , . . . ,  is the geometric progression with the first term " a ", the common ratio " r ", and the number of terms " n "
then the sum of its first n terms is
 =  =  .
Or, which is the same
=  .
In your case, a = 1, r = 4, n - 1 =  = 8 (the number of the terms); n = 9.
Substitute this data into the formula and calculate.
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On geometric progressions, see introductory lessons
- Geometric progressions
- The proofs of the formulas for geometric progressions
- Problems on geometric progressions
- Word problems on geometric progressions
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Geometric progressions".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
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