Question

(1/3)-²+(1/4)-²+(1/5)-²–(1/6)-²​

Answer 1

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ { \bigg( \frac{1}{3} \bigg)}^{ - 2} + { \bigg( \frac{1}{4} \bigg)}^{ - 2} + { \bigg( \frac{1}{5} \bigg)}^{ - 2} - { \bigg( \frac{1}{6} \bigg)}^{ - 2}}$

EVALUATION

$\displaystyle \sf{ { \bigg( \frac{1}{3} \bigg)}^{ - 2} + { \bigg( \frac{1}{4} \bigg)}^{ - 2} + { \bigg( \frac{1}{5} \bigg)}^{ - 2} - { \bigg( \frac{1}{6} \bigg)}^{ - 2}}$

$\displaystyle \sf{ = { \bigg( {3}^{ - 1} \bigg)}^{ - 2} + { \bigg( {4}^{ - 1} \bigg)}^{ - 2} + { \bigg( {5}^{ - 1} \bigg)}^{ - 2} - { \bigg( {6}^{ - 1} \bigg)}^{ - 2}}$

$\displaystyle \sf{ = {3}^{2} + {4}^{2} + {5}^{2} - {6}^{2} }$

$\displaystyle \sf{ =9 + 16 + 25 - 36}$

$\displaystyle \sf{ = 50 - 36}$

$\displaystyle \sf{ = 14}$

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