Q2-Σ Notation Review notation by investigating In this problem we will remind ourselves of 2k k O a) Consider the similar finite sum 2* k-0 Using n - 3, rewrite this expression in expanded form,...
Q2-Σ Notation Review notation by investigating In this problem we will remind ourselves of 2k k O a) Consider the similar finite sum 2* k-0 Using n - 3, rewrite this expression in expanded form, and then evaluate it. b) Rewrite Expression (2) in expanded form for n-6, and then evaluate it c) Expression (2) becomes a better approximation to Expression (1) as n grows larger. To get an idea of what (1) is, evaluate (2) using n 100. Don't compute this by hand; instead, use www.wolframalpha.com and type in summation from k 0 to 100 of 1/2A k There's no need to write down the long answer, but with it in mind, what do you think is the sum in (1)? d) Another way to approach this is using a geometric picture. Imagine each term fraction of a square (so the first term is an entire square, the second represents a term is a rectangle with area 5, the third term is a rectangle with area 7, etc.). Draw a picture with adjacent such rectangles and interpret the geometric series as an area. Is it consistent with your work above?
Q2-Σ Notation Review notation by investigating In this problem we will remind ourselves of 2k k O a) Consider the similar finite sum 2* k-0 Using n - 3, rewrite this expression in expanded form, and then evaluate it. b) Rewrite Expression (2) in expanded form for n-6, and then evaluate it c) Expression (2) becomes a better approximation to Expression (1) as n grows larger. To get an idea of what (1) is, evaluate (2) using n 100. Don't compute this by hand; instead, use www.wolframalpha.com and type in summation from k 0 to 100 of 1/2A k There's no need to write down the long answer, but with it in mind, what do you think is the sum in (1)? d) Another way to approach this is using a geometric picture. Imagine each term fraction of a square (so the first term is an entire square, the second represents a term is a rectangle with area 5, the third term is a rectangle with area 7, etc.). Draw a picture with adjacent such rectangles and interpret the geometric series as an area. Is it consistent with your work above?