Examine the convergence of the seriesSolutionGiven The serie

Examine the convergence of the series

Solution

Given

The series converges to zero

Since limit n tends to infinite

And a₀=1 and a₁=2, the general term is

a_n=a_n-1+a_n-2 for n>=2

So we can find a_3,a_4,......

a₃=a₂+a₁

   ₌₁₊₂

   ₌₃

_{like these we can all values}

_{when limit xtends to infinite 1/infinite}

_{equal to zero}

_{so the given ffunction converges}