CMSC 250 Study Guide - Midterm Guide: Prime Number, Prime Factor

103 views3 pages

Document Summary

This is a classic proof by weak induction. Step 3: now we have to prove that p(k+1) is true ie. for any (cid:883): pro(cid:448)e that (cid:1005)+(cid:1006)+(cid:1007)+(cid:1008)+(cid:1009)+ +n=(cid:4666)+(cid:2869)(cid:4667)(cid:2870) Step 2: assume p(k) is true for (cid:883). That is, assume the sum will be (cid:4666)+(cid:2869)(cid:4667)(cid:2870) From step 2, we have (cid:4666)+(cid:2869)(cid:4667)(cid:2870) +(cid:4666)+(cid:883)(cid:4667)= (cid:4666)+(cid:2869)(cid:4667)(cid:4666)+(cid:2870)(cid:4667) (cid:2870) (cid:4666)+(cid:883)(cid:4667)(cid:4672)(cid:2870)+(cid:883)(cid:4673)=(cid:4666)+(cid:2869)(cid:4667)(cid:4666)+(cid:2870)(cid:4667) (cid:2870) ( ) (1 + x) n 1 + nx. holds for any n z+. Base case: for n = 1, the left and right sides of ( ) are both. Induction step: let k z+ be given and suppose ( ) is true. + 1)x + k(cid:2870) (by algebra) 1 + (k + 1)x (since k(cid:2870) 0). integer x, (1 + x) n 1 + nx. Let x be a real number in the range given, namely x > 1. We will prove by induction that for any positive integer n, for n = k.

Get access

Grade+20% off
$8 USD/m$10 USD/m
Billed $96 USD annually
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
40 Verified Answers

Related Documents

Related Questions