Ques. -5
If α , β are the roots of 3 7 5 x 2 − 2 5 x − 2 = 0 and S n = α n + β n , then find the value of n → ∞ lim r = 1 ∑ n S r
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1 solution
How lazy I am?! Darn me! I got the answer till 3 4 8 2 9 but then didn't even bother to factor it and simplify it to 1 2 1 . Ah!
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Thanks for sharing your experience Kartik ,I'll remember not to make this mistake in JEE !!!
same here i have also done this mistake
same here, perfect options for jee mains. @Sandeep Bhardwaj
Same here dude.
SAME HERE !!
I agree that 1 2 1 is a correct option. But, why is 3 4 8 2 9 incorrect? Given that the question is silent about the numerator and denominator being co-prime/or not, I think this problem has two options being valid solutions.
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But then if we tick "None of these" making 3 4 8 2 9 correct, it makes 1 2 1 incorrect which is of course wrong.
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Hey, when are your Boards starting ? Or have they started ?
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@A Former Brilliant Member – Oh, they have already started. Today was the first. Well, I think you must be knowing that the board system is over now(though it will resume from next year or so)
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@Kartik Sharma – Actually I didn't know that . Best of Luck for your other exams :)
If you want , you can comment here .
Gotta go , bye .
My point was that the 'incorrect choices' were not properly selected.
If the choices for sin ( π / 6 ) are given as c o s ( π / 3 ) , 4 2 , 0 . 5 and none of these, then the problem is in formulating the options.
Hi @Mudit, Could you brief the steps. I got stuck in step after expansion.
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I just used formula for summation of infinite G.P. as both alpha and beta are between -1 and 1
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Thanks. How you get 29 and 348? How you find sum and product
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@Sridhar Muruganandham – α + β = a − b , α β = a c
Doing Great..keep it up @mudit bansal
Amazing solution!! Upvoted!
A suggestion is that you modify the question to "to write the answer in the simplest form" this would save a lot of incorrect answers since the objective of the questions presented here are to test mathematical knowledge not to check the computational ability of an individual. An example where logic is more important the Computation.
Oh my bad... I got 3 4 8 2 9 , then carelessly ticked 3 5 8 2 9
Notice that − 1 < α , β < 1 .Hence, on expanding n → ∞ lim r = 1 ∑ n S r we get: α + β + α 2 + β 2 + . . . = 1 − α α + 1 − β β = 1 − ( α + β ) + α β α + β − 2 α β Now on putting sum and product of roots we get: 3 4 8 2 9 = 1 2 1