How to show by default Contributions Tab in Contact Summary Page?
I don't think CiviCRM allows this out of the box, but you can achieve this by following the below steps using JavaScript:


Using JavaScript check to see if the page url have '/civicrm/contact/view?reset=1&amp;cid='
Then set below two attributes in  to true:

aria-selected="true"
 aria-expanded="true"

Where id = tab_contribute


Example:

&lt;li id="tab_contribute" class="crm-tab-button ui-corner-all livePage ui-tabs-tab ui-corner-top ui-state-default ui-tab ui-tabs-active ui-state-active crm-count-1" role="tab" tabindex="0" aria-controls="ui-id-23" aria-labelledby="ui-id-22" aria-selected="true" aria-expanded="true"&gt;

If your CMS is drupal, you can use JS Injector module to include javascript which provides functionality to run JS on specific pages.

Let me know if you need more help.