Permutations and Combinations

Permutations and Combinations

Question

Evaluate:

space space sum from straight i equals 1 to 10 of open square brackets open parentheses 1 half close parentheses to the power of straight i minus 1 end exponent plus open parentheses 1 fifth close parentheses to the power of straight i plus 1 end exponent close square brackets

Answer
space space space space sum from straight i space equals space 1 to 10 of open square brackets open parentheses 1 half close parentheses to the power of straight i minus 1 end exponent plus space open parentheses 1 fifth close parentheses to the power of straight i plus 1 end exponent close square brackets space equals space open square brackets open parentheses 1 half close parentheses to the power of 0 space plus space open parentheses 1 fifth close parentheses squared close square brackets space plus space open square brackets open parentheses 1 half close parentheses to the power of 1 plus open parentheses 1 fifth close parentheses cubed close square brackets
                                                          plus open square brackets open parentheses 1 half close parentheses squared space plus space open parentheses 1 fifth close parentheses to the power of 4 close square brackets space plus space........ space plus space open square brackets open parentheses 1 half close parentheses to the power of 9 space plus space open parentheses 1 fifth close parentheses to the power of 11 close square brackets
equals space open square brackets 1 plus 1 half plus 1 over 2 squared plus..... plus space 1 over 2 to the power of 9 close square brackets space plus space open square brackets 1 over 5 squared plus 1 over 5 cubed plus 1 over 5 to the power of 4 plus...... plus space 1 over 5 to the power of 11 close square brackets
<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> = 2 open parentheses 1 minus 1 over 2 to the power of 10 close parentheses space plus space 1 over 20 open parentheses 1 minus 1 over 5 to the power of 10 close parentheses

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