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Question

93+103+113+...+203= ____

A
42804
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B
44100
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C
45396
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D
42840
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Solution

The correct option is A 42804
Note that 93+103+113+...+203=[13+23+...+203][13+23+...+83]

The sum of cubes of first n natural numbers is given by
Sn=[n(n+1)2]2.
13+23+...+203=[20(20+1)2]2 =44100
13+23+...+83=[8(8+1)2]2 =1296

93+103+113+...+203=441001296=42804

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