Many are ensuring that ¼ is the value of the limit. That is not in the option however.
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Royal Alok Jha , 4 Years ago
Grade 12th pass
Differential Calculus> Many are ensuring that ¼ is the value of ...
1 Answers
Aditya Gupta
Last Activity: 4 Years ago
simply write the expression inside limit as
(∑r=1n r*∑k=1n-r+1 k)/n^4
= (∑r=1n r*(n – r+1)(n – r+2))/2n^4
apply KINGS rule to simplify this as
(∑r=1n (1+n – r)*(r)(r+1))/2n^4
= (∑r=1n r(r+1)(n+1 – r))/2n^4
now simply open the brackets r(r+1)(n+1 – r) and find its sum (since ∑r, ∑r^2, ∑r^3 are known) and then finally apply the limit.
you will get the ans as (1/3 – 1/4)/2
= 1/24
KINDLY APPROVE :))
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