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Question

Question: 31<sup>3</sup> + 32<sup>3</sup> + ………… + 50<sup>3</sup> =...

313 + 323 + ………… + 503 =

A

1409400

B

1409000

C

1408400

D

None

Answer

1409400

Explanation

Solution

Let

313 + 323 + 333 + ……. + 503 = S50 – S30

= (50(50+1)2)2−(30(30+1)2)2\left( \frac { 50 ( 50 + 1 ) } { 2 } \right) ^ { 2 } - \left( \frac { 30 ( 30 + 1 ) } { 2 } \right) ^ { 2 }

= 1625625 – 216225 = 1409400