Prove this limit

**concern** · November 10th, 2009, 05:11 AM

Hello, can anyone give any hint regarding this? I'm lost.

Prove that if Lim an = p
n-->infinity
then,
Lim ( a1 + a2+ .......an )/n = p
n-->infinity

Can't get started.

**concern** · November 10th, 2009, 06:59 AM

hey, can we use supremum and infemum concept here?

**Opalg** · November 10th, 2009, 07:51 AM

Originally Posted by concern

Hello, can anyone give any hint regarding this? I'm lost.

Prove that if Lim an = p
n-->infinity
then,
Lim ( a1 + a2+ .......an )/n = p
n-->infinity

Can't get started.

Replacing $a_n$ by $b_n = a_n - p$ (for all n), you reduce the problem to the case where p=0. The proof for that case is given in this thread.

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