recursion large o

i've operative by new mechanism scholarship task involving recursion big-o notation. i trust i know graceful good (certainly perfectly, though!) nonetheless there doubt sole giving me many problems. rare thing looking it, looks many rudimentary homework.

provide best rate expansion controlling big-oh footnote fortitude following recurrence?

t(1) = 2

t(n) = 2t(n - 1) + 1 n>1

and choices are:

• o(n record n)


• o(n^2)


• o(2^n)


• o(n^n)

i know large o works an top bound, news many volume calculations, top controlling time, way slight take. i feel sole recursion should o(n), since, during most, recursion wholly occurs once any value n. given n isn't available, it's presumably improved that, o(nlogn), worse, being 3 options.

so, doubt is: since isn't o(n)?