SOLUTION: Simplify: {{{(1/4) + (1/4^2) + ((4^2)/(4^3)) + ((4^2)/(4^4)) + ((4^4)/(4^5)) + ((4^4)/(4^6))}}} + ... + {{{((4^102)/(4^103)) + ((4^102)/(4^104))}}}

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Question 1199206: Simplify: + ... +
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

+ ... +

+ ... +
+ ... +

Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
Simplify: + ... +
~~~~~~~~~~~~~~~~~~~~~~~~~

I see two sequences alternate.


After separating, one sequence is    +  +  + . . . +          (1)


              Another sequence is    +  +  + . . . +          (2)


Sequence (1), after reducing, is the sum of  = 52 equal addends, each of which is  ,
so this sum is  .


Sequence (2), after reducing, is the sum of  = 52 equal addends, each of which is  ,
so this sum is  .


Therefore, the total sum is   +  =  +  =  =  = 16 = 16.    ANSWER


Solved.



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