Add Decreasing Series

Home 1 + 2 + ... + n 1 + 3 + 5 + ... + 2n-1 a+(a+b)+...+(a+nb) 1 + 4 + 9 + ... + n^2 1^3 + 2^3 +...+ n^3 1^3 - 2^3 + 3^3 -...+ n^3 Add Decreasing Series Sub Decreasing Series Add Infinite Series Finding The Next Term Finding The nth Term Add Factorials

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Adding A Sequence In The Form: 1/a + 1/a2 +...+ 1/an

   A.  This sequence reduces to the following:

               1  +  1  +...+  1  =  (an - 1)/(a-1)

               a      a2          an             an

   B.  Use the following rules:

1.  To find the numerator, subtract 1 from the denominator of the last fraction and divide by (a-1).

2.  The denominator of the answer is the same as the last denominator in the series.

Ex [1]  1  +  1  +...+ 1  =

          2      4          64    __________.

a.  The numerator is equal to the following:  (64-1)/(2-1) = 63.

b.  The denominator is 64.

c.  The answer is 63/64.

Ex [2]  4-1  +  4-2  + 4-3  + 4-4 =__________.

a.  The last number is 44 or 162 = 256.  See Squares.

b.  The numerator is (256-1)/(4-1) = 255/3 = 85.

c.  The denominator is 256.

d.  The answer is 85/256.