



 
James, For problems like this, the key idea is to write abs(a_{1} + a_{2} + ... + a_{n}) = abs(a_{1} + a_{2} + ... + (a_{n1} + a_{n})). The expression on the right hand side is a sum of n1 terms. That lets you use the induction hypothesis to get <= abs(a_{1}) + abs(a_{2}) +...+ abs(a_{n1}+a_{n}) and then apply the base case to the last term. Good luck.  


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