Question

I need to know the equations of these were n = 1

1) 1/2 - 1/4 + 1/8 - 1/16 + . . .

2) 1 + 2 + (2^2)/2 + (2^3)/6 + (2^4)/24 + (2^5)/120 + . . .

3) 0 + 3 + 8 + 15 + 24 + . . .

Answer 1

1/2 - 1/4 + 1/8 - 1/16 + =

1/2[1 - 1/2 + (1/2)^2 - (1/2)^3+... ]

1/2 1/(1+1/2) = 1/3

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2) exp(2)

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3) This is clearly divergent.

Answer 2

but what I need is actually formulas that involve n..i cant describe it

Answer 3

are you looking for the general term?

for 1)
1/2 - 1/4 + 1/8 - 1/16
GT = (-1)^(n+1)/2^n , where n = 1,2,3 ...

then 1/2 - 1/4 + 1/8 - 1/16 +
= [sigma] (-1)^(n+1)/2^n where n goes from 1 to ∞

let me know if this is what you are after.