za said:
for the induction question
c how u get:
5.5^k > 4.4^k + 3.3^k
can u divide it all by 5. ending with:
5^K > (0.8)4^k + (0.6)3^k
then u can say, seeing as though 5^k > 4^k + 3^k, then it is obviuosly greater than (0.8)4^k + (0.6)3^k.
???????????????????
nah you sub in from the S(k) thing that 5<sup>k</sup>>4<sup>k</sup>+3<sup>k</sup>
5<sup>k+1</sup>
5*5<sup>k</sup>
sub in and you get that this is less than 5<sup>k+1</sup>, thus if this works then 5<sup>k+1</sup> must work
5(4<sup>k</sup>+3<sup>k</sup>)
now 5*4<sup>k</sup>>4*4<sup>k</sup>=4<sup>k+1</sup>
and 5*3<sup>k</sup>>3*3<sup>k</sup>=3<sup>k+1</sup>
5*3<sup>k</sup>+5*4<sup>k</sup>>3<sup>k+1</sup>+4<sup>k+1</sup>
:. 5<sup>k+1</sup>>4<sup>k+1</sup>+3<sup>k+1</sup>