Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.2 Representing Functions - 1.2 Exercises - Page 26: 86

Answer

a) See table b) The set of all natural numbers c) $n=45$

Work Step by Step

We are given the factorial function: $S(n)=1+2+....+n$ a) Build a table of the function for n=1,2,...,10. $f(1)=1$ $f(2)=1+2=3$ $f(3)=1+2+3=6$ $f(4)=1+2+3+4=10$ $f(5)=1+2+3+4+5=15$ $f(6)=1+2+3+4+5+6=21$ $f(7)=1+2+3+4+5+6+7=28$ $f(8)=1+2+3+4+5+6+7+8=36$ $f(9)=1+2+3+4+5+6+7+8+9=45$ $f(10)=1+2+3+4+5+6+7+8+9+10=55$ b) The domain of the function $S(n)$ consists of all the natural numbers (positive integers). c) Compute $S(n)$ until we reach 1000: $S(30)=1+2+...+30=465$ $S(40)=1+2+...+40=820$ $S(41)=1+2+...+41=861$ $S(42)=1+2+...+42=903$ $S(43)=1+2+...+43=946$ $S(44)=1+2+...+44=990$ $S(45)=1+2+...+45=1035$ Therefore the least value for which S(n)>1000 is n=45.
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