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I would like some help proving the following result. Thanks for any help in advance.

Let $(x_{n})_{n=1}^\infty$ be i.i.d. random variables, c some nonzero constant, >and let 0 < $b_{n} \rightarrow \infty$. Prove that if $(\sum_{j=1}^{n} x_{j}) / b_{n} \overset {p}{\to} C$, then $b_{n}$~ $b_{n+1}$

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    what does $b_n \sim b_{n+1}$ maen? Also, could provide some additional context? – 2017-01-16
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    $b_{n}$~ $b_{n+1}$ means that $b_{n}$ / $b_{n+1}$ goes to 1 as n goes off to infinity. – 2017-01-16

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