Sub 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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Subtracting A Sequence In The Form: 1/a - 1/a2 -...- 1/an

A.  To solve this sequence the denominator is always an, and the numerator is:

(an-1 - an-2 -...- a - 1)

B.  Basically what this says is take the next to last denominator and subtract every value to its left from that then subtract 1.

C.  Examples

Ex [1]  1/2 - 1/4 - 1/8 - 1/16 = __________

a.  The denominator is 16.

b.  The numerator is 8 - 4 - 2 - 1 = 1.

c.  The answer is 1/16.

Ex [2]  1/4 - 1/16 - 1/64 - 1/256 = __________

a.  The denominator is 256.

b.  The numerator is 64 - 16 - 4 - 1 or 64 - 20 - 1 = 43.

c.  The answer is 43/256.

D.  In problems like Ex [1] where the denominator are 2n, the answer will always be 1/2n.

 

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