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Question

Let a1,a2,...,a100 be non-zero real numbers such that a1+a2+...+a100=0. Then


Correct Answer
A
100i=1ai2ai>0 and 100i=1ai2ai<0   
Your Answer
B
100i=1ai2ai0 and 100i=1ai2ai0   
Your Answer
C
100i=1ai2ai0 and 100i=1ai2ai0    
Your Answer
D
the sign of 100i=1ai2ai or 100i=1ai2ai depends on the choice of ai's   

Solution

The correct option is A 100i=1ai2ai>0 and 100i=1ai2ai<0   
For every real number  ai,ai2ai>ai  &  ai2ai<ai100i=1ai2ai>100i=1ai  &  100i=1ai2ai<100i=1ai100i=1ai2ai>0  &  100i=1ai2ai<0   

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