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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="normsp_1.html#NM2" title="NORMSP_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:14"/>
<font color="Maroon" title="c2">seq</font> is <a href="bhsp_4.html#V1" title="BHSP_4:attr.1">summable</a>
 ;<br/>

<a NAME="E2:14"/><b>then </b>
 <a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c2">seq</font> is <a href="bhsp_2.html#V1" title="BHSP_2:attr.1">convergent</a>
 
<b>by </b><i><a class="ref" href="bhsp_4.html#D2" target="_self" title="BHSP_4:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E3:14"/>
 <a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c2">seq</font> is <a href="bhsp_3.html#V2" title="BHSP_3:attr.2">bounded</a>
 <b>by </b><i><a class="ref" href="bhsp_3.html#T24" title="BHSP_3:th.24">BHSP_3:24</a></i>;<br/>


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