00:01
So, here we are given the series, summation n varying from 1 to infinity, 6n to the power 5 over n to the power 12 plus 1.
00:13
Estimate the series below within the value of 0 .0001.
00:20
So, we have to find the minimum value of n for necessary to estimate this s of n.
00:27
So, let's suppose s of n less than 2, integration of 6n to the power 5 divided by n to the power 12 plus 1 and the limits will go from capital n to infinity.
00:45
So, let where b tends to what? the infinity.
00:51
So, hence s of n would become equals to the limit b tends to infinity integration n to b 6n to the power 5 divided by the n to the power 12 plus 1.
01:07
Now, we suppose consider the n to the power 6 is equals to t.
01:13
So, 6n to the power 5 will become equals to dt.
01:18
While if you see the lower limit will be equals to n to the power 6 and upper limit will become b to the power 6.
01:29
So, s of n would becomes limit b tends to infinity will be as it is.
01:36
Integration lower limit will become n to the power 6 and this will become b to the power 6 and here it will be dt over t square plus 1.
01:47
So, let us find the integral here...