what is the following sum? 1 1 ⋅ 2 + 1 2 ⋅ 3 + 1 3 ⋅ 4 + . . . + 1 ( n − 1 ) ⋅ n

Question

what is the following sum?      1          1      ⋅      2        +      1          2      ⋅      3        +      1          3      ⋅      4        +  .  .  .  +      1          (      n      −      1      )      ⋅      n

Teagan Gamble · Accepted Answer

This can be written as      ∑          2              n            1          n      (      n      −      1      )      Let n = 2we have sum = 1/2 * 1/1 = 1/21/( n ( n-1) ) can be written as 1/n-1 - 1/nThus the entire expression can be written as1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/( n-1) - 1/nWe only have first and last term leftSum : 1 - 1/n= ( n-1 ) / nAnswer :             n      −      1        n

nuseldW4r · Accepted Answer

This can be written as1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/( n-1) - 1/n= 1 - 1/n= ( n-1) / n

what is the following sum? 1/12+1/23+1/34+...+1/(n-1)1

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