Let y(n)(x) = x^(2) + (x^(2))/(1+x^(2))+...

Let `y_(n)(x) = x^(2) + (x^(2))/(1+x^(2))+(x^(2))/((1+x^(2))^(2))+......(x^(2))/((1+x^(2))^(n-1))and y(x) = lim_(n rarr oo) y_(n) (x)`. Discuss the continuity of `y_(n)(x)(n = 1, 2, 3....n) and y(x) "at x" = 0`

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The correct Answer is:

`y_(n)(x)` is continuous at x = 0 for all n and y(x) is discontinuous at x = 0

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