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The value of 52 + 62 + .... + 102 + 202 is :
Answer & Solution
Correct Answer:
Option
A
= 52 + 62 + .... + 102 + 202
= (12 + 22 + 32 +..... + 102) - (12 + 22 + 32 + 42) + 400
= $$\frac{1}{6}$$ n(n + 1) (2n + 1) - (1 + 4 + 9 + 16) + 400, where n = 10
= $$\left( {\frac{1}{6} \times 10 \times 11 \times 21} \right)$$ - 30 + 400
= (385 - 30 + 400)
= 755
= (12 + 22 + 32 +..... + 102) - (12 + 22 + 32 + 42) + 400
= $$\frac{1}{6}$$ n(n + 1) (2n + 1) - (1 + 4 + 9 + 16) + 400, where n = 10
= $$\left( {\frac{1}{6} \times 10 \times 11 \times 21} \right)$$ - 30 + 400
= (385 - 30 + 400)
= 755
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