Write the sum of the series : 2 + 4 + 6 + 8 + ….. + 2n

Find the locus of the mid-point of the portion of the x cos α + y sin α = p which is intercepted between the axes.

If O is the origin and Q is a variable point on y² = x, Find the locus of the mid-point of OQ.

Write the sum of the series : 1² – 2² + 3² – 4² + 5² – 6² + ……. + (2n – 1)² – (2n)²

Write the sum to n terms of a series whose rth term is: r + 2^r