P2 Questions
using expansions20021121
Questions set at about P2 standard and length, so 14-16 marks each.
1. A G.P. has as its fifth and sixth terms 4.26 and 5.39. Find the a, the r and the twentieth term.
(ii) Expand (1+x)-1 & hence simplify ln2 +(ln2)² + (ln2)³ + ……
(iii) Show that ln2 + ln2² + ln2³ + …… + ln230 is an A.P. & find this value.
(iv) Show that ∑ ln2r = n ln2 + ln n!
2 Expand to include the term in x³,
(i) (1-2x) –1
(ii) (1+3x) –2
(iii) 1 .
(1-2x)(1+3x) ²
3(i) The series S is defined as 1-4k²+16k³ –64k⁴+…. Find the sum of this series and state the range of values of k for which this is a valid definition.
For the case where k = 1/16, find
(ii) the infinite sum,
(iii) the sum of the first six terms, and
(iv) the number of terms needed to bring the total to within a millionth of the infinite sum.
4 is there enough already? I think so.
