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Sum of sequences, product of fractions, ¢²1/(k*(k+1))

ÀÛ¼ºÀÚ Uploader : fatman ÀÛ¼ºÀÏ Upload Date: 2019-08-16º¯°æÀÏ Update Date: 2019-08-27Á¶È¸¼ö View : 285

Separate terms using partial fractions.

¢²1/(k*(k+1)) = ¢²(1/k - 1/(k+1))

Summing from k=1 to k=n,

Sum = 1 - 1/2 + 1/2 - 1/3 + 1/3 - ¡¦ - 1/(n+1)
  = 1 - 1/(n+1)
  = n/(n+1)


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Sum = n/(n+1)
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