Questions and Answers of Cambridge International AS & A Level Further Mathematics

Find 22 + 42 + … +(2n)2.Hence find 12 - 22 + 32 - 42 + (2n)2, simplifying your answer.
Determine the value of 1 – 2 + 3 - 4 + …. + (2n — 1) — (2n).
Find the number of vertical asymptotes for the following curves. a.b. yニマ- 5x -6
Find the sum of the terms 12 + 22 + 32 + 52 + 62 + 72 + ... + 972 + 982 + 992.
Without using a calculator, find, in terms of n, an expression for 1 =1(* + 3)(r + 4)
Without using a calculator, find a simplified expression for 12 + 22 – 32 + 42 + 52 – 62 + … + (3n – 2)2 + (3n – 1)2 – (3n)2.
Use the method of differences to show that Deduce that 1 1 (2r + 1)(2r + 3) 6 2(2N + 3)
Without using a calculator, given that 1 n +1 S, = E (2r + 1)(2r + 3)' show that S,= %3! 2n + 3
Find, in terms of n, an expression for 2n E r(r+ 1). ド=n+1
Leta. Find, in terms of n, an expression for Sn.b. Given that S = limn→∞Sn, write down the value of S.c. Find the range of values of n such that S – Sn < 0.001. Σ 1 S, = r=4 - 5r + 6
Find the sum of the cubes of the first 100 even terms.
Without using a calculator, determine the value of 4 Σ r=2 - 1 %3D2
Show thatHence, find the result of n(4n? + 13n + 13) 2(2r + 1)(3r + 2) = 2 r=1

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