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Home Q & A Board Science-Related Homework Help Mathematics
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Dyhtps Dyhtps
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10 years ago
If  f(r) = 1/(r(r+1)) , obtain and simplify  f(r+1)–f(r). Hence,find ∑1/(r(r+1)(r+2))

f(r+1)-f(r) = 1/((r+1)(r+2)) - 1/(r(r+1))
                 = -2/(r(r+1)(r+2))
1/(r(r+1)(r+2))  = (-  1/2)[ f(r+1)-f(r) ]
∑  1/(r(r+1)(r+2)) = (- 1/2)∑ [f(r+1)-f(r)]
                     = (- 1/2)[ f(n+1)-f(1)]
                      = (- 1/2)[ 1/((n+1)(n+2)) - 1/2 ]
                      = (n(n+3))/(2(n+1)(n+2))

still, I got the wrong answer..why?
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wrote...
#1
Educator
10 years ago
Hi there, not sure if this helps.
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#2
Valued Member
On Hiatus
10 years ago
With a quick glance I found a mistake over there:
Quote
= (- 1/2)[ 1/((n+1)(n+2)) - 1/2 ]
                      = (n(n+3))/(2(n+1)(n+2))
It seems that you forgot to multiply with (-1/2)
The rest seems correct to me.
Is that what you were looking for?
Dyhtps Author
wrote...
#3
10 years ago
yeah, kind of made a mistake when summing 2 fractions up.. Face with Stuck-out Tongue
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