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The first thought when trying to solve such a problem is that you might be able to write this sum as a geometric progression. Luckily, it is the case here as well, as we can observe that S is the derivati...

To show something is a subgroup we need to show that it satisfies the group axioms. Therefore we need to show that if g and h are in Z(G) then gh is in Z(G), g^-1 is in Z(G), the identity e is in Z(G). As...

Polar coordinates are expressed in the form (r,θ), where r is the distance of the point, P, from the origin, and θ (usually expressed in radians) is the angle between the line joining the point to the ori...

We know to find roots of any quadratic equation we use the quadratic formula, [-b +- (b^2 - 4ac)^(1/2)]/2a where a=2, b=6, and c=7.

Plug these values in and we obtain, [-6 +- (-20)^(1/2)]/4. [Remem...

We first find the complementary function by guessing y=e^(kx). Substituting this into the equation d^2y/dx^2 + (3/2)dy/dx + y = 0. we find k^2 + (3/2)k + 1 = 0 which factorises into (k+2)(k+1/2). So our c...