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# is this tru? watch

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1. does (1-r)(r^n) = 1-r^(n+1)??

if so can someone show me how
2. put r = 2
n = 3

(1 - 2)(2^3) = -8
1 - 2^(3+1) = -15

so no.

However,
(1-r)(r^n) = r^n - r*r^n
= r^n - r^(n+1)
3. then is :

(1-r)(1+r+r^2+r^3+....r^n) = 1-r^(n+1)

i think its true but not sure how
4. (Original post by popat)
then is :

(1-r)(1+r+r^2+r^3+....r^n) = 1-r^(n+1)

i think its true but not sure how
LHS
= (1 - r) + (1 - r)r + (1 - r)r^2 + (1 - r)r^3 + ... + (1 - r)r^n
= (1 - r) + (r - r^2) + (r^2 - r^3) + (r^3 - r^4) + ... + (r^n - r^(n + 1))
= 1 - r^(n + 1)
= RHS

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Updated: November 11, 2004
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