How to find 1 + 1 2 + 1 3 + 1 4 + 1 6 + 1 8 + 1 9 + 1 12 + ⋯?Find the sum of series 1 + 1 2 + 1 3 + 1 4 + 1 6 + 1 8 + 1 9 + 1 12 + ⋯ ,where the terms are the reciprocals of positive integers whose only prime factors are two's and three's:

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How to find   1  +      1    2    +      1    3    +      1    4    +      1    6    +      1    8    +      1    9    +      1    12    +  ⋯?Find the sum of series  1  +      1    2    +      1    3    +      1    4    +      1    6    +      1    8    +      1    9    +      1    12    +  ⋯  ,where the terms are the reciprocals of positive integers whose only prime factors are two&#039;s and three&#039;s:

toroipanfz · Accepted Answer

Hint: factor      ∑          i      =      0        ∞        ∑          j      =      0        ∞        1                  2        i                    3        j            as the product of a sum over   i and a sum over   j

Larissa Hart · Accepted Answer

∑          k      =      0              ∞            1          2      k            ∑          k      =      0              ∞            1          3      k        =      1          1      −              1        2              ⋅      1          1      −              1        3              =  3

Find the sum of series 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+... where the terms are the reciprocals of positive integers whose only prime factors are two's and three's:

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