Question

1^2-2^2+3^2-4^2+........... sum into n terms​

Answer 1

Answer:

Step-by-step explanation:let 'x' be number of odd numbers in n terms & let 'y' be number of even numbers in n terms therefore x+y=n

sum of x odd numbers is given by x(2x+1)(2x-1)/3

and sum of y even numbers is given by 2y(y+1)(2y+1)/3

thus question is {sum of n odd numbers - sum of n even numbers}

∴ sum of n terms = [x(2x+1)(2x-1)/3]-[2y(y+1)(2y+1)/3]-----------------eq1

if x=y i.e x=y=z then eq1 becomes -z(2z+1), where z is number of equal odd and even numbers