If the series UN converges to s, then the series (UN + UN + 1) converges to s

If the series UN converges to s, then the series (UN + UN + 1) converges to s

By
   ∑(n>=1)u(n) = s,
Available
   ∑(n>=1)[u(n)+u(n+1)]
  = ∑(n>=1)u(n) + ∑(n>=1)u(n+1)
  = 2s-u(1).