(Solved): Evaluate the following sum. \[ \sum_{k=1}^{50}\left[(k+2)^{2}-k^{2}\right] \] \[ \sum_{k=1}^{50}\le ...
Evaluate the following sum. \[ \sum_{k=1}^{50}\left[(k+2)^{2}-k^{2}\right] \] \[ \sum_{k=1}^{50}\left[(k+2)^{2}-k^{2}\right]= \] (Simplify your answer.)
Evaluate the integral. \[ \int_{0}^{\frac{\pi}{3}}(\cos x+\sec x)^{2} d x \] \[ \int_{0}^{\frac{\pi}{3}}(\cos x+\sec x)^{2} d x= \] (Type an exact answer, using \( \pi \) as needed.)