Maths WorkshopMaths problems with full solutions

Find the sum

12 problems · Evaluating Convergent Series: Examples and Problems

Search problems Level

Ex.208Geometric series and repeating decimals

#geometric series #decimals #sum

Ex.209Geometric series with a parameter

#geometric series #convergence domain #parameters

Ex.372Splitting the sum of 1/n² into even and odd terms

#absolute convergence #rearrangement #pi squared

Ex.385Series with factorials and the number e

#exponential series #factorials #e

Ex.388Telescoping series with partial fractions

#telescoping #partial fractions #sums

Ex.389Telescoping with logarithms

#telescoping #logarithm #divergence

Ex.390Telescoping with a shift p

#telescoping #partial fractions #harmonic numbers

Ex.1393Three logarithmic series

#logarithmic series #telescoping #conditional convergence

Ex.1395Three convergent series with explicit sums

#geometric series #telescoping #arctangent identity #d'Alembert

Ex.1396Three series with computed sums

#geometric series #telescoping #arctan identity

Ex.1510The Euler-Mascheroni constant as a series

#Euler-Mascheroni constant #harmonic numbers #telescoping #logarithm

Ex.2074Rearranging a conditionally convergent series

#conditional convergence #rearrangement #Riemann theorem #ln 2