C = 1 + 52 + 53 + 54 + ... + 5200
5C = 5. ( 1 + 52 + 53 + 54 + ... + 5200 )
5C = 5 + 53 + 54 + 55 + ... + 5201
5C - C = ( 5 + 53 + 54 + 55 + ... + 5201 ) - ( 1 + 52 + 53 + 54 + ... + 5200 )
4C = 5 + 5201 - ( 1 + 52 )
4C = 5201 + 5 - 26
4C = 5201 - 21
⇒ C = \(\dfrac{5^{201}-21}{4}\)