F fredinho New Member Joined Apr 17, 2009 Messages 17 Gender Male HSC 2009 May 5, 2009 #1 Question 15 Chapter 8.2 Find the sum of the first 10 terms of the series 3+7+13+...+[2^n+(2n-1)]
Fortify ♪웨딩드레스 Joined Mar 20, 2007 Messages 1,281 Gender Male HSC 2009 May 5, 2009 #2 Split [2^n + (2n-1)]; so: A = 2^n and b = (2n-1) So A = 2^1 + 2 ^ 2 + 2 ^ 3 + ... + 2^10 A = 2 (2^10 - 1) / (2 - 1) = 2046 Now: B = (2(1)-1) + (2(2)-1) + ... + (2(10)-1) B = 1 + 3 + ... + 19 B = 10/2 (1+19) B = 100 Therefore: S10 = A + B = 2146.
Split [2^n + (2n-1)]; so: A = 2^n and b = (2n-1) So A = 2^1 + 2 ^ 2 + 2 ^ 3 + ... + 2^10 A = 2 (2^10 - 1) / (2 - 1) = 2046 Now: B = (2(1)-1) + (2(2)-1) + ... + (2(10)-1) B = 1 + 3 + ... + 19 B = 10/2 (1+19) B = 100 Therefore: S10 = A + B = 2146.