Fractional Infinite Series

Find the following sum:

∞

(x²+x)

x=1

View the solution

Fractional Infinite Series Solution

∞

x² + x

x=1

∞

x(x+1)

x=1

∞

x+1

x=1

(By the method of partial fractions)

This obviously tunnels: (

) + (

)...

leaving just 1.

Or, with more vigor:

x+1

x=1

= 1 -

n+1

and the limit of this as n goes to ∞ is 1.

Solution submitted by PdoX

A Sequence of Circles

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