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a 4u qus on series and sequences (1 Viewer)
- Thread starter lollol
- Start date
see the attachment
Wackedupwacko
Member
i just woke up so my brains still in first gear ... but that first part is definately an induction question. you will need the gp formula : Sn = a(r^n -1) / r - 1 . basically start with let k =1 and then prove when k+1 to hold true as well if k is true and done. part ii) just substitute, use demoirves theorem for the angles. rearrange the RHS with the given eqn and it should come out nice and pretty.
P
pLuvia
Guest
1. You don't need induction for the first part. Just use the GP formula, then you can take out the 1/(1-z)
Thus you are left with
[1/(1-z)][n.sig.k=1(1-zk)
Then you can split the sigma bit and simplify from there
2. Use DeMoivre's theorem and bash that algebra. Start off with z=cos@+isin@, lm(z)=sin@
lm(zk)=sink@
lm[n.sig.k=1][z+z2+...+zk)
Then this should turn out as your wanted LHS, now use the assumption of the z/(1-z) then manipulate this assumption and simplify it
Thus you are left with
[1/(1-z)][n.sig.k=1(1-zk)
Then you can split the sigma bit and simplify from there
2. Use DeMoivre's theorem and bash that algebra. Start off with z=cos@+isin@, lm(z)=sin@
lm(zk)=sink@
lm[n.sig.k=1][z+z2+...+zk)
Then this should turn out as your wanted LHS, now use the assumption of the z/(1-z) then manipulate this assumption and simplify it