Add Infinite 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 Infinite Sequences In The Form: a + a/b + a/b2 + ...

A.  Adding sequences of this nature reduces to the following:

 a + a/b + a/b2 + ...  =   a 

                                 1 - r

where a is the first term of the sequence and r is whatever a is being multiplied by, (in this case 1/b).

B.  Look at the following examples:

Ex [1]  2 + 1 + 1/2 + ... = _________.

a.  In this example 'a' is 2 since this is the first term and 'b' is 1/2 since every term is being multiplied by 1/2.

b.  According to the formula this is equal to 2/(1 - 1/2) which equals 2/(1/2) which equals 4.

c.  The answer is 4.

Ex [2]  6 + 4 + 8/3 + ... = __________.

a.  In this example 'a' is 6 and 'b' is 2/3.

b.  According to the formula this is equal to 6/(1 - 2/3) = 6/(1/3) = 18.

c.  The answer is 18.

Ex [3]  12 - 4 + 4/3 - ... = __________.

a.  In this example 'a' is 12 and 'b' is -1/3.

b.  According to the formula this is equal to 12/(1 - -1/3) = 12/(4/3) = 9.

c.  The answer is 9.

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