Exercise 4.1 2. Establish each of the following for all n ≥ 1 by the Principle of Mathematical Induction. Solution a) S(n): ==‚ S(1): = = =1‚ So S(1) is true. Assume S(k): = Consider S(k+1) = = +=-1+= -1. Hence‚ it follows that S(k)⇒S(k + 1) is true for all n ∈ Z+ by the Principle of Mathematical Induction. b) S( n) for n=1‚ = 2 = 2+(1-1). So S(1) is true. Inductive Step: assume S(k)is true‚ for some (particular) k ∈ Z+—that is‚ assume that =2+(k-1). For n=k+1‚ = + (k+1)
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Henry Heimlich is an American Thoracic Surgeon‚ and is also known for creating the “Heimlich Maneuver”. Heimlich was a very smart intelligent man. He has thought of ways to save lives today that no one else would have thought of. Dr. Heimlich invented the chest drain valve‚ gastric tube operation and much more. Thankfully for this man today doctors have saved thousands of lives. Heimlich was born on February 1920 (age 95)‚ Wilmington‚ Delaware. (Henry Heimlich). Before fame he graduated from Cornell
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From the play written by John Patrick Shanley and titled Doubt: a Parable‚ the readers get a central question‚ asking whether certainty can be equated to truth or not. From one side‚ some hints outlining the fact that certainty can be equated to truth are evident. On the other side‚ there are doubts as to whether certainty can be equated to truth. The doubt is thus left unresolved. The play begins with father Flynn’s sermon lecturing regarding certainty as he claims‚ “Doubt can be a bond as powerful
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Holley 1 Adam Holley Professor Richardson ENC 1101 B001 June 27 2012 Reading Response 1 “If readers construct the meaning of texts‚ how does information transmission work?” Through constructing the meaning of texts‚ a reader can interpret and summarize chunks of writing into something that is already processed by the reader. Personally‚ I know that if I begin reading a piece of text that I have never researched or learned in the past‚ obviously I cannot make an information transmission. On
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Henry VII of England The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man. [George Bernard Shaw] Innovation is the process of creating something new. Innovation is impossible without passion. Innovators ultimately see the world differently. Innovators end up becoming obsessed with taking the world from as it is to as it should be. Many innovators in the for-profit sector focus
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Stephen Fernandes Professor Grayson November 27‚ 2011 The Missing Meaning In The First Part of King Henry IV‚ Shakespeare included some meaningful comedy with the character Falstaff and his relationship with Prince Harry. Falstaff was Prince Harry’s rebellious‚ cunning‚ and very fat friend whom Harry associated himself with to get a bad reputation amongst the people in his land. Throughout the story these characters interacted with each other‚ and constantly chat and banter back and forth over
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Biography - An Account of his life (1879-1981) Reverend Henry Ward was born in Golden Grove‚ St. Ann. He received his early education at Clapham Elementary School‚ and then moved on to St. George’s Elementary in guys Hill. There he passed the Pupil Teachers’ Examination with distinction and gained an exhibitioner’s scholarship to the Micro Teachers’ College. He distinguished himself at Mico‚ and his personal conduct was exemplary throughout his college career. In 1900‚ he graduated from Mico as
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Was the reign of Henry VII the financial highpoint of the Tudor era? Henry VII came to the throne in 1485; in many ways his reign appeared vulnerable and his finances poor‚ however‚ when he died in 1509 he left his son Henry a sound fiscal legacy. However‚ was his reign destined to be the financial high point of the Tudor dynasty he founded? The accession of a strong king and the apparent conclusion of civil war meant many had high hopes that Henry VII could restore stability to the country. The
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An emergency occurs when a urgent situation takes place that can be detrimental to a person’s life. Emergencies are not a common occurrence; however do arise on occasion. The response and outcome of emergencies can be positively amplified with an organized plan or preparedness technique. In “The Neighborhood” community‚ there was an emergency‚ forest fires‚ which left the residents to experience unfortunate residual respiratory effects. The many that suffered include patients and staff in the hospital
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Pimsucha K. Ms. Amy Angelo English III Honors 20/11/17 Response to Literature: The Minister’s Black Veil Romanticism is a period of aritistic‚ aesthetic‚ imagination‚ and individualism. It orginated in the late eighteenth century. The Minister’s Black Veil‚ a parable by Nathaniel Hawthorne is one of the literature which reflects the concept of romanticism. The Minister’s Black Veil is a story about Reverend Hooper‚ a minister in Milford‚ New England. Hooper delivered a sermon while wearing a
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