IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

ashish17

If a₁ = 1 and a_n+1 = , n>=1, and if a_n = a. Find the value of a ?

sreenivasarao

since at infinity an+1=an so let X=4+3x/3+2x than solve for x that is the answer man

Ekns

is ans= square root of 2 ???

ashish17

@ Ekns

ur ans is correct please post the sol.

spideyunlimited

sreenivasarao has given the correct method. At n tending to infinity, a_n and a_n+1 will be qual (since infinity + 1 = infinity)

so just equate

a = 4 + 3a / 3 + 2a
4 = 2a^2
a = rt(2) ..... (can't be negative looking at the positive series)

hsbhatt

I just want to correct this impression that it always holds true that $a_n = a_{n+1}$ as $n \rightarrow \infty$ (the reason being that $\infty+1 = \infty$ ). This is true only if the sequence is convergent.

For example, try the sequence a_k= (-1)^k

So, it is important to see if the limit exists before making this assumption.

Here, it is given that the limit exists and so you can assume that $a_n = a_{n+1}$ = a as $n \rightarrow \infty$

spideyunlimited

nl

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