Maths WorkshopMaths problems with full solutions

Power series

9 problems · Radius of convergence and sums of power series.

Ex.332Radius of convergence
#power series #ratio test
Power series
L2
L2
Ex.772Power series of ln(1+x) and arctan x
#integration term by term #Leibniz series #ln 2
Power series
L2
L2
Ex.773Radius of convergence, four examples
#radius of convergence #ratio test #endpoints
Power series
L2
L2
Ex.775Solving y″ = −y with a power series
#differential equations #power series #cosine #recurrence
Power series
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L2
Ex.776Summing power series in closed form
#power series #differentiation term by term #closed form
Power series
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L2
Ex.1490The generating function of Fibonacci numbers
#generating function #Fibonacci #partial fractions #radius of convergence
Power series
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L2
Ex.1499A series of functions
#series of functions #normal convergence #pointwise convergence
Power series
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L2
Ex.1506The generating function of central binomial coefficients
#binomial series #generalised binomial coefficients #radius of convergence
Power series
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L2
Ex.1511e^x e^y = e^(x+y) from power series
#Cauchy product #exponential series #binomial theorem
Power series
L2
L2