Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Mathematics
Mathematics
Problem Which of the following gives the Maclaurin series representation of cos ( 4 x ) \cos(4x) cos ( 4 x ) ∑ n = 0 ∞ ( − 1 ) n 16 n x 2 n ( 2 n ) ! \displaystyle \sum_{n=0}^{\infty} (-1)^{n}\,\dfrac{16^{\,n} x^{2n}}{(2n)!} n = 0 ∑ ∞ ( − 1 ) n ( 2 n )! 1 6 n x 2 n ∑ n = 0 ∞ ( − 1 ) n 4 n x 2 n ( 2 n ) ! \displaystyle \sum_{n=0}^{\infty} (-1)^{n}\,\dfrac{4^{\,n} x^{2n}}{(2n)!} n = 0 ∑ ∞ ( − 1 ) n ( 2 n )! 4 n x 2 n ∑ n = 0 ∞ ( − 1 ) n 16 n x 2 n + 1 ( 2 n + 1 ) ! \displaystyle \sum_{n=0}^{\infty} (-1)^{n}\,\dfrac{16^{\,n} x^{2n+1}}{(2n+1)!} n = 0 ∑ ∞ ( − 1 ) n ( 2 n + 1 )! 1 6 n x 2 n + 1 ∑ n = 0 ∞ ( − 1 ) n 16 n x 2 n n ! \displaystyle \sum_{n=0}^{\infty} (-1)^{n}\,\dfrac{16^{\,n} x^{2n}}{n!} n = 0 ∑ ∞ ( − 1 ) n n ! 1 6 n x 2 n Browse the problem library