IIT JEE , AIEEE Forum - Mathematics , Algebra

man111

(1) _{[r =1 ]}^{[ infinity]} tan-1(1/r²) and there is no mistake in this question and explain fully.

hsbhatt

If the answer is something like tan^-1(tan

- tanh

/tan

+tanh

) where

=

/

2 it is probably best not to go into the solution!

man111

yes you are saying absolutely write.

but sir i want asolution for this problem.

hsbhatt

once konichiwa had asked this problem. A few days later I was going through S L Loney Part II and I saw this problem in one of the exercises in the book. The hint involved using some infinite series about which you need not bother. Its not worth it, just take my word.

Mein sirf itna poochna chahtha hoon ki aise problem par samay vyarth kyon karte ho. Meri baat maan is qn par aur aage badhne ki koi zaroorat nahi hain

sandeepramesh

the infinite series of tan^-1 x ?

konichiwa2x

Consider the expansion of

Notice that the general term is

.

Hence,

.

is a very famous result for which I have listed the proof below.

konichiwa2x

TO PROVE:

PROOF:

Now, the roots of

occur at

where

Hence we can factorise as follows:

Multiply out the products and collect the coefficients of

to see that it is equal to

But from the original expansion of

, the coefficient of

is

Hence both are equal

.

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