Summation of n terms of a series$ 1+2+8+64+.........$

Asked Sep 23 '15 at 06:53

Active Sep 23 '15 at 07:05

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In one of my problem , I got a series as $1$,$2$,$8$,$64$,$1024$...and so on. can we really get a sum expression for that series$???$

If yes, then what is the expression $f$ $?$ or the sum of $n$ terms of a series $$1+2+8+64+1024+......+2^{n(n+1)/2}$$ What is the procedure to get expression??

edited Sep 23 '15 at 07:05

user118494

5,837

asked Sep 23 '15 at 06:53

Ajay shifu

2

There isn't a closed form using plain arithmetic. The last term is far too big compared to the previous ones. – user21820 Sep 23 '15 at 06:57
There is apparently a recurrence: $a(n) = a(n-1) + \dfrac{2(a(n-1) -a(n-2))^2}{a(n-2) - a(n-3)} $ – Henry Sep 23 '15 at 07:08
@Henry. Could you explain how you did arrive to this nice result ? It is quite impressive. – Claude Leibovici Sep 23 '15 at 07:50
@ClaudeLeibovici: not mine but Robert Israel's at OEIS A181388 – Henry Sep 23 '15 at 07:53

Summation of n terms of a series$ 1+2+8+64+.........$

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