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Shraddhey Srivastava Grade: 12
        

limn->infinty [1/na + 1/(na+1) + 1/(na+2) + ...... + 1/nb]


Plz show the method. Ans is -> log (b/a).


This question is from arihant, last workbook exercise of Limits.

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Shraddhey


this type of question is solved by hepl of intigration


limn->∞ [1/na + 1/(na+1) + 1/(na+2) + ...... + 1/(na+nb-na)]


limn->∞ 1/(na+r)               r  vary from 0 to (b-a)


limn->∞ 1/nn/(na+r)               r  vary from 0 to (b-a)


limn->∞ 1/n1/(a+r/n)               r  vary from 0 to (b-a)


now if any given series is of this form then replace ∑  by ∫   ,and  r/n   by  x , and  1/n by dx


=ob-a  dx/(a+x) 


=lnb/a


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Badiuddin         

7 years ago
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