@@BlackTshirtMathProfessor but then Y did u did the second example for comparison test by splitting the integral, u could hav simply said that the lower limit could be any real number greater than 0 and say it is same as the previous one and ended the video?
I hav a doubt in p integral in that u had put the limit as[ 1 to ∞ )but are we allowed to put the limit as [X to ∞) where X is any real number > 0 ?
That’s correct! It’s typically the starting index of the infinite series sum. Usually this is 0 or 1.
@@BlackTshirtMathProfessor but then Y did u did the second example for comparison test by splitting the integral, u could hav simply said that the lower limit could be any real number greater than 0 and say it is same as the previous one and ended the video?
It’s due the improper integral that we’re comparing with. The integral of 1/x^3 from 0 to infinity diverges due to x = 0.
@@BlackTshirtMathProfessor oh ok thanks for help👍
You’re welcome, Manoj!