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Please explain Vn method with example and ALGORITHM ..?

Please explain Vn method with example and ALGORITHM ..?

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1 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
9 years ago
Hii

The method of differences is used when we are not given the sum of the series. For example, if we wanted to find the sum, ∑nr=1ur of some series where the terms follow some certain pattern. The aim of the method of differences is to express the rth term, which will be a function of r as the difference of two expressions in r of the same form. What this means is that we write the term ur in the form f(r)−f(r+1) or even f(r+1)−f(r), where f(r) is some function of r. If we can express ur in such a way we can see quite simply that
u1+u2=f(1)−f(2)+f(2)−f(3)=f(1)−f(3)
We can extend this idea further to find
r=1u1=f(1)−f(2)
r=2u2=f(2)−f(3)
r=3u3=f(3)−f(4)
r=n−1un−1=f(n−1)−f(n)
r=nun=f(n)−f(n+1)
Now we can see if we add all of these togetheru1+u2+u3+⋯+un−1+un=f(1)−f(2)+f(2)−f(3)+f(3)−f(4)+⋯+f(n−1)−f(n)+f(n)−f(n+1)=f(1)−f(n+1)


Best of Luck

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