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Category > Architecture and Design Posted 17 May 2017 My Price 4.00

Critical Thinking Prove that n2 + 5n is divisible by 2 for all positive integral values of n

1. Restate the conjecture that 8n - 1 is divisible by 7 for all positive integers n using the definition of divisibility.

 

2. Critical Thinking Prove that n2 + 5n is divisible by 2 for all positive integral values of n.

 

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Alpha Geek
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Status NEW Posted 17 May 2017 01:05 PM My Price 4.00

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file 1495027193-2073273_1_636304979337413278_Mathematical-induction.docx preview (120 words )
T-----------o p-----------rov-----------e:8-----------n-1----------- is----------- di-----------vis-----------ibl-----------e b-----------y 7----------- fo-----------r a-----------ll -----------pos-----------iti-----------ve -----------int-----------ege-----------rs.----------- W-----------e w-----------ill----------- us-----------e t-----------he -----------pri-----------nci-----------ple----------- of----------- ma-----------the-----------mat-----------ica-----------l i-----------ndu-----------cti-----------on.----------- F-----------or -----------n=1----------- we----------- ha-----------ve -----------8n------------1=7----------- wh-----------ich----------- is----------- di-----------vis-----------ibl-----------e b-----------y 7-----------. -----------We -----------wil-----------l a-----------ssu-----------me -----------tha-----------t t-----------he -----------sta-----------tem-----------ent----------- ho-----------lds----------- tr-----------ue -----------for----------- n=-----------k. ----------- 8k------------1=-----------7p -----------whe-----------re -----------p i-----------s a----------- po-----------sit-----------ive----------- in-----------teg-----------er.----------- F-----------or -----------n=k-----------+1 -----------we -----------hav-----------e 8-----------(k+-----------1)------------1=8-----------k+8------------1=-----------8k+-----------7=7-----------p+7-----------=7(-----------p+1-----------) w-----------hic-----------h i-----------s d-----------ivi-----------sib-----------le -----------by -----------7. ----------- Th-----------ere-----------for-----------e t-----------he -----------sta-----------tem-----------ent----------- ho-----------lds----------- tr-----------ue -----------for----------- al-----------l n-----------. -----------Pro-----------ve -----------tha-----------t n-----------2 +----------- 5n----------- is----------- di-----------vis-----------ibl-----------e b-----------y 2----------- fo-----------r a-----------ll -----------pos-----------iti-----------ve
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