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the question is as above, I don't know how to write ic and ih. can anyone give a complete answer? appreciate it

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marked as duplicate by Adam Hughes, JMoravitz, Community Nov 18 '16 at 18:54

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    $\begingroup$ $|(z_1+\cdots+z_{n-1})+z_n|\le |z_1+\cdots+z_{n-1}|+|z_n|$ now do the same to $|z_1+\cdots+z_{n-1}|$ $\endgroup$ – user160738 Nov 18 '16 at 18:41
  • $\begingroup$ yes, but how about the steps.. it looks like a recursion $\endgroup$ – gonda Nov 18 '16 at 18:44
  • $\begingroup$ @gonda induction and recursion are fundamentally the same thing, that's just terminology. $\endgroup$ – Adam Hughes Nov 18 '16 at 18:45
  • $\begingroup$ |(z1+⋯+zn−1)+zn|≤|z1+⋯+zn−1|+|zn| is it a theorem? $\endgroup$ – gonda Nov 18 '16 at 18:49
  • $\begingroup$ can I use it directly? $\endgroup$ – gonda Nov 18 '16 at 18:49