THEOREM OBJECTIVES Recognize patterns in binomial expansions. Evaluate a binomial coefficient. Expand a binomial raised to a power. Find a particular term in a binomial expansion Understand the principle of mathematical induction. Prove statements using mathematical induction. Definition: BINOMIAL THEOREM Patterns in Binomial Expansions A number of patterns‚ as follows‚ begin to appear when we write the binomial expansion of a b n‚ where n is a positive integer. a
Premium
The United States serves as a giant puzzle. From coast to coast‚ each region of land is slowly being put together. This is very similar to westward expansion. From 1801 to1844‚ westward expansion spread rapidly and America experienced a serious change in national unity. During this period territorial expansion had a very large impact and overall brought Americans together. During the early 1800’s (1800-1823) the Louisiana Purchase and Treaty of 1818 increased national unity. The Louisiana Purchase
Free United States Louisiana Purchase Native Americans in the United States
December 1‚ 2012 Expansion of the Presidency After each president has gone through their presidency‚ ever since the Father of our country George Washington‚ the powers of the president has increased little by little. To the extent that their powers are going beyond what the Constitution and the Framers expected it to be. Our current president‚ thanks to the input from past presidents‚ has so much power he does not realize. The issue now is whether to go against this expansion of power or to
Premium President of the United States United States Congress
westward expansion was the key to the nation’s health: He believed that a republic depended on an independent‚ virtuous citizenry for its survival‚ and that independence and virtue went hand in hand with land ownership‚ especially the ownership of small farms. (“Those who labor in the earth‚” he wrote‚ “are the chosen people of God.”) In order to provide enough land to sustain this ideal population of virtuous yeomen‚ the United States would have to continue to expand.The westward expansion of the
Premium Slavery in the United States Compromise of 1850 United States
14 October 3‚ 2013 The age of Exploration affected not only Europeans in a positive way but other regions in positive but mostly negative ways. The Age of Exploration began when Columbus believe in new trade routs to India and found the Americas. There were many motives like sliver‚ gold‚ converting people‚ spices‚ and more technology. During this time Europeans affected many native populations of newly conquered lands. During the age of Exploration‚ Europeans shaped the newly conquered lands
Free Europe Colonialism New World
Accounting Exploration To most people being an accountant means sitting in an office crunching numbers all day and having little to no people skills. This could not be further from the truth. I have only recently decided that I would like to pursue a career in accounting after spending two years as a pre-medical student and realizing that I no longer had the desire to spend another ten years in school and residency programs. Accounting grabbed my attention because it does deal with a lot of numbers
Premium Accountant Employment Accountancy
The westward expansion‚ which started in the 1820s‚ was one of the biggest steps forward our country has ever taken. It nearly tripled the size of our country and increased the population by monstrous amounts. It also improved the economy greatly though agricultural means‚ prompted political leaders to sent people to explore (Lewis and Clark)‚ started a civil war‚ motivated huge amounts of people to move west‚ and almost destroyed our country. The expansion was magnified greatly by the
Free United States Native Americans in the United States Mississippi River
Purpose: In this lab‚ we will heat up a metal rod and measure how much it expands. We will calculate its Coefficient of Linear Expansion‚ α‚ and prove the formula for thermal expansion‚ ΔL = αLiΔT. Also‚ we heat up a known volume of methyl alcohol and calculate its Coefficient of Volume Expansion‚ β‚ and prove the formula for volume expansion of a liquid ΔV = βViΔT. Equipment: Hollow Metal Rods of different metals‚ Steam Generator‚ Stand‚ Burner‚ Flexible Hoses‚ Motion Amplifier‚ Micrometer
Premium Thermodynamics Temperature Measurement
The age of exploration had many varied effects on the countries involved‚ mainly Spain‚ France‚ and England. By establishing a prosperous empire in South America by conquering the native people‚ Spain became vastly wealthy off of the gold collected by its native subjects. However‚ since the native people were dying off rapidly due to the foreign diseases brought over by the Conquistadors‚ as well as malnutrition and fatigue‚ Spain and Portugal were the first to introduce slavery to the New World
Premium Native Americans in the United States Christopher Columbus Americas
Exploration Proposal This year in year 12 I would like to explore city and suburban photography. In my exploration I will focus on landscapes‚ man-made and that made by mother earth. What I hope to showcase in my portfolio this year is a collection of cityscapes hoping to capture astonishing man-made structures and the great architecture that’s been exerted into them. With this I also hope to showcase a bit of an ‘old vs. new’ theme‚ especially with many iconic Melbourne structures. I hope to also
Premium Photography Digital photography Color