Sum of fractions with consecutive integer denominators

  • Context:
  • Thread starter Thread starter Monoxdifly
  • Start date Start date
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
1 reply · 1K views
Monoxdifly
MHB
Messages
288
Reaction score
0
Does anyone know how to add these fractions?
[math]\frac1{1\times2}+\frac1{2\times3}+\frac1{3\times4}+…+\frac1{2009\times2010}[/math]
I believe making them in [math]\frac12+\frac1{6}+\frac1{12}+….+\frac1{421890}[/math] form isn’t the correct approach.
Is there anything we can cancel out?
 

Discussion

Physics news on Phys.org
Re: [ASK] Fracttion Addition

Monoxdifly said:
Does anyone know how to add these fractions?
[math]\frac1{1\times2}+\frac1{2\times3}+\frac1{3\times4}+…+\frac1{2009\times2010}[/math]
I believe making them in [math]\frac12+\frac1{6}+\frac1{12}+….+\frac1{421890}[/math] form isn’t the correct approach.
Is there anything we can cancel out?

What does Partial Fraction decomposition do for us? $\dfrac{1}{n\cdot(n+1)} = \dfrac{1}{n}-\dfrac{1}{n+1}$