Show that the following series converges and find its sum: partial sum from k =2 to infinity of 4^(k/2)*5^(2-k)

Find the sum of the series: sum_(n=0)^infinity (((-1)^n 16^(n-1))/n!)

Use the binomial series to find the first four terms of the power series representation of f(x)= 1/(1+x)^3 centered at 0. Then use those four terms to estimate 1.7^-3. Round to 4 places