Question

does anyone have any tricks to learning to solve for series questions...ratio, geometric, root, power ect?

Answer 1

The formulae for:

Sums of numbers:
\[\sum_{k=1}^{n}k = \frac{ 1 }{ 2 }n(n+1)\]

Sums of squares:
\[\sum_{k=1}^{n}k^2 = \frac{ 1 }{ 6 }n(n+1)(2n+1)\]

Sums of cubes:
\[\sum_{k=1}^{n}k^3 = \frac{ 1 }{ 4 }k^2(k+1)^2\]

Sums where k > 1:
\[\sum_{k=a}^{n}f(k) = \sum_{k=1}^{n}f(k) - \sum_{k=1}^{a-1}f(k)\]

Coefficients can be taken out of the summation:
\[\sum_{k=1}^{n}cf(k) = c \sum_{k=1}^{n}f(k)\]

are always useful when solving series with polynomials. Don't know if this is what you're looking for, though!

Answer 2

I appreciate it, that helps thanks