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since when did you start frequenting this forum xiao?

that the limiting sum of a converging geometric series.. let (1 + x + x^2 + ... + x^n) = K Kx = (x + x^2 + ... + x^(n+1) ) K - Kx = [1 - x^(n+1)] K(1-x) = [1 - x^(n+1)] K = [1 - x^(n+1)] / [1-x] and if you take limit n to infinity, x^(n+1) tends to 0. K = 1/(1-x) by the pattern...

I think 1...

hmm let's do it the otehrwise way.. 1+x+x^2 + ... = 1/(1-x) differentiating boths sides 1 + 2x + 3x^2 + 4x^3 + .... = 1/(1-x)^2 doubling both sides 2 + 4x + 6x^2 + 8x^3 + ... = 2/(1-x)^2 subtract the original identity (2 + 4x + 6x^2 + 8x^3 + ...) - (1 + x + x^2 + ...) =...

in exams you try to keep up the pace.. but when you are doing exercises, you should slow down to the point that you are not making mistakes.. that pays off in the long run

well do the substitution dx = -1/u^2 du you get integrate { sqrt(3), 1/sqrt(3) } -ln(1/u) / [( 1 + (1/u)^2 ) * ( u^2)] du simplyfy you get I = -I so.. I = 0

126 135 234 so it's 3/(9 C 3 ) 2 + 16 2 + 34 so it's 2/(8 C 2)

I was thinking about charles and carl..

I could probably tell who got it then

slow down a bit when you do exercises.

it is a reduction formula quesiton. and if you can do that .. it's probably the book's problem

don't worry. :P

(7 + 1/10)^2 = 49 + 1/100 + 14/10 > 50 therefore 2 is true

corrected to 2 decimal places. 2.) Express the volume of the solid formed by rotating the region bounded by x = 1, y = 1/x, y = e^(-x) and x = k (k>1) as a definite integral. Suppose k increases at a rate of a units per second, find the rate of change of the volume of the solid. 3.)...

it's in one of cambridge or fitzpatrick under conics sketching

you're learning maths, it isn't just for HSC

Re: Re: how are these possible mm 0.99999.... and 1.00000000 are both decimal expansions of 1.. nothing's wrong there. (there must be something between 2 different real numbers) And get a stupid answer :D

you can acquiesce :D

let length of string as a function of time be L(t) L = sqrt(h^2 + d^2) where h is the height of the kite and d is the horizontal distance of the kite from the boy. dL/dt = (dL/dd) * (dd/dt) evaluated at their respective values. dL/dt = d/sqrt(h^2 + d^2) * 8 = 80/100 * 8 = 6.4 My guess is...

wonder if there's a markup language for maths around the web..