Permutations and Combinations

Permutations and Combinations

Question

Write first five terms of the following sequence and obtain the corresponding series.

straight a subscript 1 space equals space straight a subscript 2 space equals space 2 comma space space space straight a subscript straight n space equals space straight a subscript straight n minus 1 end subscript space minus space 1, n>2

Answer

Here,        space straight a subscript 1 space equals space 2 comma space space space straight a subscript 2 equals 2.
                space space space straight a subscript straight n space equals space straight a subscript straight n minus 1 end subscript minus 1                        ...(i) (for n>2)

Putting n = 3 in (i), we get straight a subscript 3 equals straight a subscript 2 minus 1 space equals space 2 space minus space 1 space equals 1.
Putting n = 4 in (i), we get straight a subscript 4 space equals space straight a subscript 3 minus 1 space equals space 1 space minus space 1 space equals 0
Putting n = 5 in (i), we get <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>
The corresponding series is: 2 + 2 + 1 + 0 - 1 ...............

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