Question

1.3+2.4+3.5+...+99.101=???

Answer 1

1.3+2.4+3.5+...+99.101

= ( 2 -1 ). ( 2 + 1 ) + ( 3 -1) . ( 3 + 1 ) + . . . +  ( 100 - 1 ) . ( 100 + 1 )

= \(2^2\) - 1 + \(3^2\) - 1 + . . . + \(100^2\) - 1

= ( \(2^2\) + \(3^2\)+ \(100^2\) )  -  (  1 + 1 + . . . + 1 )

= ( \(2^2\) + \(3^2\)+. . . +  \(100^2\)) - 99

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