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Consider a sequence of non-negative numbers ${x_{n} : n = 1, 2, . . .}$. Which of the following statements cannot be true?

  1. $\sum ^{\infty }_{n=1} x_{n}= \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}= \infty$.
  2. $\sum ^{\infty }_{n=1} x_{n}= \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}< \infty$.
  3. $\sum ^{\infty }_{n=1} x_{n}< \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}< \infty$.
  4. $\sum ^{\infty }_{n=1} x_{n}\leq 5$ and $\sum ^{\infty }_{n=1} x_{n}^{2}\geq 25$.
  5. $\sum ^{\infty }_{n=1} x_{n} < \infty $ and $\sum ^{\infty }_{n=1} x_{n}^{2}= \infty$.
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I think (b) could be the answer, because if summation of Xn=infinite,then summation of Xn^2 cannot be less than Xn value
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