Question 959558
<pre>
Break the 60 term series up into the sum of the 30 term 
series of odd numbered terms and the 30 term series of the
even numbered terms.  That is

2+6+4+12+6+24+... = 2+4+6+... +6+12+24+... 

The first series is arithmetic and the second one is geometric:

to find the sum of 2+4+6+... to 30 terms we use the formula:

{{{S[n]}}}{{{""=""}}}{{{expr(n/2)(2a^""+(n-1)d)}}}, where {{{a[1]=2}}}, {{{n=30}}}, and {{{d=2}}}

{{{S[30]}}}{{{""=""}}}{{{expr(30/2)(2(2)^""+(30-1)2)}}} 

{{{S[30]}}}{{{""=""}}}{{{15(4^""+(29)2)}}}

{{{S[30]}}}{{{""=""}}}{{{15(4+58)}}}

{{{S[30]}}}{{{""=""}}}{{{15(62)}}}

{{{S[30]}}}{{{""=""}}}{{{930}}}

---

To find the sum of 6+12+24+... to 30 terms we use the formula:

{{{S[n]}}}{{{""=""}}}{{{(a[1](r^n-1))/(r-1)}}}, where {{{a[1]=6}}}, {{{n=30}}}, and {{{r=2}}}

{{{S[30]}}}{{{""=""}}}{{{6(2^30-1)/(2-1)}}}

{{{S[30]}}}{{{""=""}}}{{{6(1073741824-1)/(1)}}}

{{{S[30]}}}{{{""=""}}}{{{6(1073741823)}}}

{{{S[30]}}}{{{""=""}}}{{{6442450938}}}

----------------

The sum of the two sequences is  930+6442450938 = 6442451868

Edwin</pre>