MHB [ASK] Find 1/(1×2)+1/(2×3)+1/(3×4)+…+1/(2009×2010)

  • Thread starter Thread starter Monoxdifly
  • Start date Start date
AI Thread Summary
The discussion centers on finding the sum of the series 1/(1×2) + 1/(2×3) + 1/(3×4) + … + 1/(2009×2010). Participants question the effectiveness of transforming the fractions into simpler forms and explore whether any terms can be canceled. The concept of partial fraction decomposition is introduced, highlighting that 1/(n(n+1)) can be expressed as 1/n - 1/(n+1). This approach simplifies the summation process, potentially leading to a clearer solution. The conversation emphasizes the need for effective methods in summing such series.
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?
 
Mathematics 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? $\dfrac{1}{n\cdot(n+1)} = \dfrac{1}{n}-\dfrac{1}{n+1}$
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB [ASK] Addition of Fractions: 1/3+1/6+1/10+1/15+1/21+....+1/231
Replies
3
Views
2K
MHB [ASK] Find 1/(1)+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+…+2009)
Replies
1
Views
1K
MHB Solve Quadratic Equation: Find c-a Given p and q
Replies
4
Views
1K
I Alternating Harmonic Numbers are cool, spread the word!
Replies
4
Views
2K
MHB Find the exact sum of the series 1/(1⋅2⋅3⋅4)+1/(5⋅6⋅7⋅8)+....
Replies
5
Views
2K
MHB [ASK] Induction Determine the value of n if 1 + 3 + 6 + .... + n(n - 1)/2 = 364
Replies
5
Views
2K
MHB Inequality solve (x+1)/6<x-(3x-2)/4
Replies
2
Views
1K
MHB Partial fraction problem (x^2)/[(x-2)(x+3)(x-1)]
Replies
4
Views
2K
MHB Solve Exponential Equation 4^(5-9x)=1/(8^(x-2) )
Replies
7
Views
3K
MHB Solving 4(2x-1)=3(3x+2): Step 1-3
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top