Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-db.php on line 556 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/util/string.php on line 702 Deprecated: substr(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/pages/question.php on line 185 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/pages/question.php on line 198 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/app/users.php on line 1277 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/util/string.php on line 702 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/util/string.php on line 702 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/pages/question-view.php on line 473 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/util/string.php on line 702 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/util/string.php on line 702 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-base.php on line 722 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-base.php on line 722 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-base.php on line 722 2016 Test 1 Q1 - Actuarial Science Hotseat
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Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-theme-base.php on line 160 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-theme-base.php on line 162 in BUS 3024S - Contingencies by (1.7k points)

Hi, could you pleas explain how the (1-y)^-2 is obtained in the solution below. image

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-theme-base.php on line 935 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-theme-base.php on line 935

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Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-theme-base.php on line 160 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-theme-base.php on line 162 by (670 points)
Hi

Please see the last line you attached in the second image. If you differentiate sum (y^k) you will get sum (k*y^k-1). 

So sum (k*y^k-1) = first derivative of sum (y^k) = first derivative of (1-y)^-1 = - (1-y)^-2 *(-1)= (1-y) ^-2
Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-theme-base.php on line 935 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /usr/www/users/acscidewug/qa-include/qa-theme-base.php on line 935

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