You have to include following js libraries
<script src="@Url.Content("~/Scripts/jquery.unobtrusive-ajax.js")" type="text/javascript"></script>
<script src="@Url.Content("~/Scripts/jquery.validate.js")" type="text/javascript"></script>
<script src="@Url.Content("~/Scripts/jquery.validate.unobtrusive.js")" type="text/javascript"></script>
View example
<div id="result"></div>
@using (Ajax.BeginForm("Index", "Home", new AjaxOptions { UpdateTargetId = "result" }))
{
@Html.TextArea("resultText")
<input type="submit" value="OK" />
}