Permutations and Combinations

Permutations and Combinations

Question

Find the sum of all the two digit numbers, which when divided by 4, yields 1 as remainder.

Answer

All the numbers, which consist of two digits and leave 1 as remainder when divided by 4 are: 13, 17, 21, ........., 97.
Here, a = 13, d = 4, straight t subscript straight n space equals space 97
rightwards double arrow            a + (n - 1)d = 97              rightwards double arrow    13 + (n - 1) 4 = 97
rightwards double arrow       (n - 1) 4 = 97 - 13 = 84           rightwards double arrow           n - 1 = <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>  rightwards double arrow    n = 22

∴                    straight S subscript 22 space equals space 22 over 2 space left square bracket space 13 space plus space 97 right square bracket space equals space 11 space left parenthesis 110 right parenthesis space equals space 1210             left square bracket therefore space space straight S subscript straight n space equals space straight n over 2 space left parenthesis straight a space plus space straight l right parenthesis right square bracket

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