Question

What is the difference between the sum of first “n” even numbers and the sum of first “n” odd numbers?.​

Answer 1

Solution -

Sum of first n even numbers -

This is an ap with the initial term as 0 and common Difference as 2 .

S_Even - { n / 2 } { 2 × 0 + ( n - 1 ) 2 }

=> [ n / 2 ] × [ 2 ( n - 1 ) ]

=> [ n ( n - 1 ) ] × [ 2 / 2 ]

=> n ( n - 1 ) .

Sum of first n odd numbers -

This is an ap with the initial term as 1 and common Difference as 2 .

S_Odd - { n / 2 }{ 2 × 1 + ( n - 1 ) 2 }

=> { n / 2 }{ 2 + 2n - 2 }

=> { n } { 2n } / { 2 }

=> n²

Difference -

=> n ( n - 1 ) - n²

=> n² - n - n²

=> - n.

This is the required answer .

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Answer 2

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