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91.
Evaluate:

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

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

135 Views

92.

Find the sum of the products of the corresponding terms of sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, $1 half.$

165 Views

93.

If f is a function f(x + y) = f(x) f(y) for all x, y $space space element of$ N such that f(1) = 3 and $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ , find the value of n.

91 Views

94.

If A and G are respectively the A.M. and G.M. between the two distinct positive numbers are a and b, then Prove A>G.

129 Views

95.

If A and G are respectively the A.M. and G.M. between two positive numbers a and b, then proof the quardratic equation having a, b as it roots is $straight x squared minus 2 Ax plus straight G squared equals 0.$

138 Views

96.

If A and G be A.M. and G.M. between two positive numbers, then the numbers are

$straight A plus-or-minus square root of straight A squared minus straight G squared end root.$

102 Views

97.

The A.M. between two positive numbers is 34 and their GM. is 16. Find the numbers.

155 Views

98.

Find two positive numbers whose difference is 12 and whose A.M. exceeds the GM. by 2.

900 Views

99.

Find the value of n so that $fraction numerator straight a to the power of straight n plus 1 end exponent plus straight b to the power of straight n plus 1 end exponent over denominator straight a to the power of straight n plus straight b to the power of straight n end fraction$ may be the G.M. between a and b.

117 Views

100.

The A.M. of two numbers is 3 times their G.M. Show that the numbers are in the ratio

$3 plus 2 square root of 2 colon space space 3 minus 2 square root of 2.$