1n Xnn 1Solutionan1nn1 lim an1anlim nn11 so the radius of co

Solution

a_n=(-1)ⁿ/(n+1)

lim |a_n+1/a_n|=lim |n/(n+1)|=1

so the radius of convergence is 1/1=1

when x=-1

we get harmonic series 1/(n+1) which is divergent

when x=1 (-1)ⁿ/(n+1) is convergent by alternating test

So the interval of ocnvergence is [-1,1)