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Calculus/pre cal 12th exponentia and logarithmic functions II

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Question
question 1) what is the 10th term of the following sequence?
16, 4,1....

question 2) use sigma notation to write the sum of the following series
4+20+100+500+2500+12 5000

Answer
Answer to question 1)  the sequence is 16, 4, 1, 1/4, 1/16, 1/64, 1/2561/1024, 1/4096, 1/16384, ...
So the tenth term is 1/16384.

Answer to question 2)  the terms seem to follow a geometric pattern.  The next term is 5 times the previous term.  So in sigma notation (I hope you know how to write the big sigma to denote SUM, with tiny indication on the top and bottom telling people where n is starting and where it is ending), it is sum_{n=0}^{infinity}  4*5^n

Calculus

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Amos

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I can answer all calculus question. I am a Math Lecturer and I teach Math in a College, usually Calculus 1, Calculus 2 and Calculus 3 and Linear Algebra.

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I have been teaching in this college for more than 12 years. Prior to that, I taught for three years as Visiting Assistant Professor.

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I got my doctorate from Univ. of Rochester in Algebraic Toppology. I got a MA from Univ of Rochester, an MA from York Univ. in Toronto and almost did my M.Sc in the National Univ. of Singapore.

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