ON SOME SERIES INVOLVING SMARANDACHE FUNCTION

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ON SOME SERIES INVOLVING SMARANDACHE FUNCTION by

Emil Burton

The study of infinite series involving Smarandache function is one of the most interesting aspects of analysis. In this brief article me give only a bare introduction to it.

E

First we prove that the series

K=2

S(k) (kH) !

converges and has

OE]e- 22' ~r2 l

the sum

S (m) is the Smarandache function: Let

us n

~

L.J ic=2

1:' 1! 2!

denote S(k) (k+1)!

<

1 n!

1 + - + - + ... + -

1

2

S(m)

= min

by

=

k=2

n

k

implies that

show

that

as follows:

n

~

We

En'

k E--,------;--,--(k+1)!

S(k)

{kEN;.mlk!}

E

k=2

S(k) (k+1) !

13

~

E . .(k+l)! .,. . k,. .---,-n

k=2

=

1

1 (n+l) !

2!

1

1

2

(k+l) !

<

1 2


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