BuildServiceProvider does not activate service

### Type of issue

Code doesn't work

### Description

The following example is wrong:

```csharp
using Microsoft.Extensions.DependencyInjection;

var services = new ServiceCollection();

services.AddActivatedSingleton();

ServiceProvider provider = services.BuildServiceProvider();
```

BuildServiceProvider() doesn't activate the service.

### Page URL

https://learn.microsoft.com/en-us/dotnet/core/extensions/dependency-injection/auto-activation?tabs=dotnet-cli

### Content source URL

https://github.com/dotnet/docs/blob/main/docs/core/extensions/dependency-injection/auto-activation.md

### Document Version Independent Id

5bbf9150-5b16-c5e3-7207-906fa7c0c132

### Platform Id

5e9b375b-bdce-6e92-5158-77e0ccc96940

### Article author

@gewarren

### Metadata

* ID: 079daeaa-bb2a-5574-e909-225118b018a5
* PlatformId: 5e9b375b-bdce-6e92-5158-77e0ccc96940
* Service: **dotnet-fundamentals**

[Related Issues](https://github.com/dotnet/docs/issues?q=is%3Aissue+is%3Aopen+5bbf9150-5b16-c5e3-7207-906fa7c0c132)

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[Associated WorkItem - 576158](https://dev.azure.com/msft-skilling/Content/_workitems/edit/576158)