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Magazine Problem 50
Find the coefficient of \(B^{-10}\) in the expansion of \(\left[\left(B^{2} / 2\right)-\left(3 / B^{3}\right)\right]^{10}\).
Problem 50
Carry out the indicated operations. Express your results in rectangular form for those cases in which the trigonometric functions are readily evaluated without tables or a calculator. $$(1-i)^{3}$$
Problem 50
Express each of the sums without using sigma notation. Simplify your answers where possible. $$\sum_{j=2}^{5} \log _{10} j$$
Problem 51
Express each of the sums without using sigma notation. Simplify your answers where possible. $$\sum_{j=1}^{6}\left(\frac{1}{j}-\frac{1}{j+1}\right)$$
Problem 51
Carry out the indicated operations. Express your results in rectangular form for those cases in which the trigonometric functions are readily evaluated without tables or a calculator. $$(-2-2 i)^{5}$$
Problem 51
Show that the coefficient of \(x^{n}\) in the expansion of \((1+x)^{2 n}\) is \((2 n) ! /(n !)^{2}\).
Problem 52
Express each of the sums without using sigma notation. Simplify your answers where possible. $$\sum_{j=1}^{5}\left(x^{j+1}-x^{j}\right)$$
Problem 52
Find \(n\) so that the coefficients of the 11 th and 13 th terms in \((1+x)^{n}\) are the same.
Problem 52
Carry out the indicated operations. Express your results in rectangular form for those cases in which the trigonometric functions are readily evaluated without tables or a calculator. $$\left(-\frac{1}{2}+\frac{1}{2} \sqrt{3} i\right)^{6}$$
Problem 53
Carry out the indicated operations. Express your results in rectangular form for those cases in which the trigonometric functions are readily evaluated without tables or a calculator. $$(-2 \sqrt{3}-2 i)^{4}$$
