7 real exam questions with step-by-step video solutions · Try each question yourself first, then open the video solution to check your working. Stuck? Ask Axi below – it knows this page’s questions.
New · Axi
Stuck on a series question?
Axi, our AI tutor, answers questions on any series problem on this page – no copying, no pasting, no sign-up.
What are you stuck on? Ask about any series question on this page and I will talk you through it.
Axi answers from this page’s question, tutorial and worked solution. Live Axi reads and marks your own working in the app.
1EDEXCEL FP1 June 2014 Q5
(a) Use the standard results for sum_{r=1}^{n} r and sum_{r=1}^{n} r^2 to show that sum_{r=1}^{n} (2r-1)^2 = (1/3)n(4n^2 - 1) for all positive integers n. (6) (b) Hence show that sum_{r=2n+1}^{4n} (2r-1)^2 = an(bn^2 - 1) where a and b are constants to be found. (3)
View video solution (2 parts)
Part (a):
Part (b):
2EDEXCEL FP1 June 2013 Q5
(a) Use the standard results for sum_{r=1}^{n} r and sum_{r=1}^{n} r^2 to show that sum_{r=1}^{n} (r+2)(r+3) = (1/3)n(n^2 + 9n + 26) for all positive integers n. (6) (b) Hence show that sum_{r=n+1}^{3n} (r+2)(r+3) = (2/3)n(an^2 + bn + c) where a, b and c are integers to be found. (4)
View video solution (2 parts)
Part (a):
Part (b):
3EDEXCEL FP1 January 2013 Q1
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
View video solution (1 part)
Part (a):
4EDEXCEL FP1 January 2011 Q5
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
View video solution (2 parts)
Part (a):
Part (b):
5EDEXCEL FP1 June 2010 Q9
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
View video solution (3 parts)
Part (a):
Part (b):
Part (c):
6Edexcel A Level June 2019 Paper 2 Q8
(i) Find the value of sum_{r=4}^{infinity} 20 x (1/2)^r. (3) (ii) Show that sum_{n=1}^{48} log_5((n+2)/(n+1)) = 2. (3)
View video solution (1 part)
Part (a):
7Edexcel A Level June 2023 Paper 2 Q2
A sequence u1, u2, u3, ... is defined by u1 = 35 and u_{n+1} = u_n + 7cos(n pi/2) - 5(-1)^n. (a)(i) Show that u2 = 40. (ii) Find the value of u3 and the value of u4. (3) Given that the sequence is periodic with order 4, (b)(i) write down the value of u5, (ii) find the value of sum_{r=1}^{25} u_r. (3)
