i) Given that , where n is an integer, prove that

ii) Hence find In in terms of n.

I can do the first part.

How do i do the second part?

thank you.

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- Jun 14th 2011, 01:33 AMBabyMiloReduction formulae
i) Given that , where n is an integer, prove that

ii) Hence find In in terms of n.

I can do the first part.

How do i do the second part?

thank you. - Jun 14th 2011, 01:54 AMemakarovRe: Reduction formulae
Note that , write several first values of and try to guess the general formula for .

- Jun 14th 2011, 02:06 AMBabyMiloRe: Reduction formulae
In= -n*-(n-1)*-(n-2)....

is this correct? - Jun 14th 2011, 02:11 AMemakarovRe: Reduction formulae
- Jun 14th 2011, 02:16 AMBabyMiloRe: Reduction formulae
can you explain step by step?

im feeling stupid :)

thank you. - Jun 14th 2011, 02:30 AMemakarovRe: Reduction formulae
Starting from and calculating subsequent values of using the recurrence equation , we get

As you noted, , which, by definition, is . Further, we note that for odd n and for even n. The sequence shows a similar behavior with respect to alternating signs. Altogether, .