I know the answer is 499, but cannot figure out how to get there: Find the following sum:81+64+54+48+36+36....

Question

amistre64 · Answer

does it means the mirror image?

anonymous · Answer

Or are you looking for a sequence?

anonymous · Answer

sequence. It's a question from the 2001 Math Team problem set

amistre64 · Answer

86543, 1412, 26(0)
14486, 167,      28
                    --------
                       288

might not be my idea

amistre64 · Answer

to get a 9 youd need a .5 from that end and it aint got that

amistre64 · Answer

the ... presupposes it goes to infinity

amistre64 · Answer

81  64   54   48   36   36
   17   10    6    12    0
       7      4     6    12
           3      2     6
                1     4
                    3

differences dont seem to help

amistre64 · Answer

81    64    54    48    36    36
9(9)  8(8)  9(6) 4(12)  6(6)  9(4)
       4(16)        2(24)
       9(7)+1     9(5)+3

hmmm

anonymous · Answer

I got it:
$$\sum_{n=1}^{\infty}2^{n-1}3^{5-n}+\sum_{n=1}^{\infty}3^{n-1}2^{8-2n}$$

anonymous · Answer

which if you evaluate is 499

anonymous · Answer

Thanks for all the help guys! You got us thinking along the tracks we needed (my math team was looking at this problem and we couldn't figure out why the answer was 499)