## hw

Suppose $$\lim_{n \rightarrow \infty} a_{n} = L$$ let $$m_{n}=(\sum_{1}^{n}a_{k})/n.$$ Show that $$\lim_{n\rightarrow \infty}m_{n}=L$$

• The proof is very simple
we have lim n--> infinity An= L
so we can use this for all values of n when n tends to infinity
so we have the sequence
(summation 1 to n) Ak/n = (A1 + A2+ A3....... An)/n
this is less or equal to
(An + An +.......An)/n
so when n tends to infinite we can use A1 =A2 = A3= ..... = An each
so we get
(summation 1 to n) Ak/n = (A1 + A2+ A3....... An)/n
=(An + An +.......An)/n
=> nAn/n
=> An
taking limits we get
L
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