College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises - Page 601: 45

Answer

$S_n=\sqrt{1}-\sqrt{n+1}$

Work Step by Step

We know that $a_n=\sqrt n-\sqrt{n+1}$ First term is given as $a_1=\sqrt{1}-\sqrt{2}$ Second term is given as $a_2=\sqrt{2}-\sqrt{3}$ Third term is given as $a_3=\sqrt{3}-\sqrt{4}$ Fourth term is given as $a_4=\sqrt{4}-\sqrt{5}$ Now $S_1=a_1=\sqrt{1}-\sqrt{2}$ $S_2=a_1+a_2=\sqrt{1}-\sqrt{3}$ $S_3=a_1+a_2+a_3=\sqrt{1}-\sqrt{4}$ $S_4=a_1+a_2+a_3+a_4=\sqrt{1}-\sqrt{5}$ Thus, $S_n=\sqrt{1}-\sqrt{n+1}$
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