sum of perfect square between 120 to 300
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Lowest perfect square between 120 and 300 is 121=11²
Highest perfect square between 120 and 300 is 289=17²
Therefore, sum of perfect squares between 120 and 300
=11²+12²+⋯+17²=(1²+2²+⋯+17²)−(1²+2²+⋯+10²)
=17(17+1)(2×17+1)/6−10(10+1(2×10+1)/6
=17×18×35/6−10×11×21/6
=1785−385
=1400
Highest perfect square between 120 and 300 is 289=17²
Therefore, sum of perfect squares between 120 and 300
=11²+12²+⋯+17²=(1²+2²+⋯+17²)−(1²+2²+⋯+10²)
=17(17+1)(2×17+1)/6−10(10+1(2×10+1)/6
=17×18×35/6−10×11×21/6
=1785−385
=1400
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