Uninitialized constant API on rake routes - ruby-on-rails

Question

Following this tutorial, I created the API of my existing blog web application on Rails. I am getting the error:
uninitialized constant API
This is my code:
lib/api/v1/articles.rb:
module API
module V1
class Articles < Grape::API
version 'v1'
format :json
resource :articles do
desc "Return list of recent posts"
get do
Article.recent.all
end
end
end
end
end
lib/api/v1/root/rb
module API
module V1
class Root < Grape::API
mount API::V1::Articles
end
end
end
lib/api/root.rb
module API
class Root < Grape::API
prefix 'api'
mount API::V1::Root
end
end
lib/tasks/routes.rake
namespace :api do
desc "API Routes"
task :routes => :environment do
API::Root.routes.each do |api|
method = api.route_method.ljust(10)
path = api.route_path.gsub(":version", api.route_version)
puts " #{method} #{path}"
end
end
end
config/routes.rb
Rails.application.routes.draw do
mount API::Root => '/'
get 'welcome/index'
root 'welcome#index'
resources :articles
end
This is the existing web application code:
app/controllers/articles_controller.rb
class ArticlesController < ApplicationController
def new
end
def create
# render plain: params[:article].inspect
#article = Article.new(article_params)
#article.save
redirect_to #article
end
def show
#article = Article.find(params[:id])
end
private
def article_params
params.require(:article).permit(:title,:text)
end
end
Now I'm in the Accessing API routes part of this article. When I run rake routes it gives the error, uninitialized constant API.. What I'm doing wrong.
Edit: As per the comment, giving the detailed error
rake aborted!
NameError: Uninitialized constant API
F:/blog/config/routes.rb:2:in 'block in <top (required)>'
F:/blog/config/routes.rb:1:in '<top (required)>'
C:in 'execute_if_updated'
F:/blog/config/environment.rb:5:in '<top (required)>'
Tasks: TOP =>routes =>environment
Contents of environment.rb
# Load the Rails application.
require File.expand_path('../application', __FILE__)
# Initialize the Rails application.
Rails.application.initialize!
When I insert config.autoload_paths += Dir["#{config.root}/lib/**/"] in your config/application.rb, and run rake routes, it gives the error can't convert Symbol into String
Upgrading the grape version, I got this error:

Answer 1

As per the discussion, you need to update your grape gem's version to 0.9.0 and then you need to add this line in your Gemfile:
gem 'grape', '0.9.0'
and then:
$ bundle install

Answer 2

As of version 0.11.0, the documentation says
Rails
Place API files into app/api. Rails expects a subdirectory that
matches the name of the Ruby module and a file name that matches the
name of the class. In our example, the file name location and
directory for Twitter::API should be app/api/twitter/api.rb.
Simple solution would be creating another api folder and moving entire files & dirs into app/api/api folder