P2 Expansions 20021121

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 –64k+….  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.

© David Scoins 2017