Fun with infinite sums - Haacked!

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// Install FSharp.Charting package from NuGet
// and then reference the charting library for
// easy visualization from F# Interactive
#load @"packages\FSharp.Charting.0.90.5\FSharp.Charting.fsx"
open FSharp.Charting

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/// Generates partial sums of the reciprocal series
/// First generate series, then use scan for partial sums
let eulerSums =
  Seq.initInfinite (fun i -> 1.0 / float (i + 1) ** 2.0) 
  |> Seq.scan (+) 0.0

/// Generate partial sums of grandi series (even easier!)
let grandiSums = 
  Seq.initInfinite (fun i -> -1.0 ** float i)
  |> Seq.scan (+) 0.0

/// Generate partial sums of the grandiSums series
/// using the cesaro summation (simply take the sums
/// and divide by the element index in mapi)
/// (We skip the initial zero elements produced by scan) 
let grandiCesaro = 
  grandiSums
  |> Seq.skip 1
  |> Seq.scan (+) 0.0
  |> Seq.mapi (fun i partial -> partial / float i )
  |> Seq.skip 1

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// Take 100 (or whatever number of elements)
// and pass the series to Chart.Line to see a chart  
eulerSums
|> Seq.take 100
|> Chart.Line

// Same for the other visualizations!
grandiSums   |> Seq.take 100 |> Chart.Line
grandiCesaro |> Seq.take 100 |> Chart.Line

Multiple items
namespace FSharp

--------------------
namespace Microsoft.FSharp

namespace FSharp.Charting

val eulerSums : seq<float>

Full name: Script.eulerSums


 Generates partial sums of the reciprocal series
 First generate series, then use scan for partial sums

module Seq

from Microsoft.FSharp.Collections

val initInfinite : initializer:(int -> 'T) -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.initInfinite

val i : int

Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = System.Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>

val scan : folder:('State -> 'T -> 'State) -> state:'State -> source:seq<'T> -> seq<'State>

Full name: Microsoft.FSharp.Collections.Seq.scan

val grandiSums : seq<float>

Full name: Script.grandiSums


 Generate partial sums of grandi series (even easier!)

val grandiCesaro : seq<float>

Full name: Script.grandiCesaro


 Generate partial sums of the grandiSums series
 using the cesaro summation (simply take the sums
 and divide by the element index in mapi)
 (We skip the initial zero elements produced by scan)

val skip : count:int -> source:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.skip

val mapi : mapping:(int -> 'T -> 'U) -> source:seq<'T> -> seq<'U>

Full name: Microsoft.FSharp.Collections.Seq.mapi

val partial : float

val take : count:int -> source:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.take

type Chart =
  static member Area : data:seq<#value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:Color * ?XTitle:string * ?YTitle:string -> GenericChart
  static member Area : data:seq<#key * #value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:Color * ?XTitle:string * ?YTitle:string -> GenericChart
  static member Bar : data:seq<#value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:Color * ?XTitle:string * ?YTitle:string -> GenericChart
  static member Bar : data:seq<#key * #value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:Color * ?XTitle:string * ?YTitle:string -> GenericChart
  static member BoxPlotFromData : data:seq<#key * #seq<'a2>> * ?Name:string * ?Title:string * ?Color:Color * ?XTitle:string * ?YTitle:string * ?Percentile:int * ?ShowAverage:bool * ?ShowMedian:bool * ?ShowUnusualValues:bool * ?WhiskerPercentile:int -> GenericChart (requires 'a2 :> value)
  static member BoxPlotFromStatistics : data:seq<#key * #value * #value * #value * #value * #value * #value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:Color * ?XTitle:string * ?YTitle:string * ?Percentile:int * ?ShowAverage:bool * ?ShowMedian:bool * ?ShowUnusualValues:bool * ?WhiskerPercentile:int -> GenericChart
  static member Bubble : data:seq<#value * #value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:Color * ?XTitle:string * ?YTitle:string * ?BubbleMaxSize:int * ?BubbleMinSize:int * ?BubbleScaleMax:float * ?BubbleScaleMin:float * ?UseSizeForLabel:bool -> GenericChart
  static member Bubble : data:seq<#key * #value * #value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:Color * ?XTitle:string * ?YTitle:string * ?BubbleMaxSize:int * ?BubbleMinSize:int * ?BubbleScaleMax:float * ?BubbleScaleMin:float * ?UseSizeForLabel:bool -> GenericChart
  static member Candlestick : data:seq<#value * #value * #value * #value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:Color * ?XTitle:string * ?YTitle:string -> CandlestickChart
  static member Candlestick : data:seq<#key * #value * #value * #value * #value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:Color * ?XTitle:string * ?YTitle:string -> CandlestickChart
  ...

Full name: FSharp.Charting.Chart

static member Chart.Line : data:seq<#value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:System.Drawing.Color * ?XTitle:string * ?YTitle:string -> ChartTypes.GenericChart
static member Chart.Line : data:seq<#key * #value> * ?Name:string * ?Title:string * ?Labels:#seq<string> * ?Color:System.Drawing.Color * ?XTitle:string * ?YTitle:string -> ChartTypes.GenericChart