106this is a QOD.
http://targetiit.com/iit_jee_forum/posts/28th_december_2008_1566.html
Q. how would we prove that that the following statement is wrong
n+n+n......n times = n2
differentiatng both sides w.r.t n we get
1+1+1+.....n times = 2n
or n=2n
or 1=2
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4 Answers
10611)you cannot differentiate.. because this function is defined only at some points...
it is not even a continuous function.
so there is no question of taking derivatives
2)Secondly because the number of terms also vary with x
1=1/x+1/x+1/x+1/x+....+1/x x times
differentiating both sides
0=-1/x2+(-1/x2)+(-1/x2)+....+(-1/x2) x times
0=-1/x
this could only be a possibillity but only possible if the above condition is not taken into consideration
