#### Answer

$\sum ^{20}_{i=1}\left( -1\right) ^{i-1}\times \left( \dfrac {1}{i}\right) ^{2}$

#### Work Step by Step

$1-\dfrac {1}{4}+\dfrac {1}{9}-\dfrac {1}{16}\ldots -\dfrac {1}{400}=\left( -1\right) ^{1-1}\times \left( \dfrac {1}{1}\right) ^{2}+\left( -1\right) ^{2-1}\times \left( \dfrac {1}{2}\right) ^{2}+\left( -1\right) ^{3-1}\times \left( \dfrac {1}{3}\right) ^{2}+\ldots \left( -1\right) ^{20-1}\times \left( \dfrac {1}{20}\right) ^{2}=\sum ^{20}_{i=1}\left( -1\right) ^{i-1}\times \left( \dfrac {1i}{i}\right) ^{2}$