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Evaluate 1/400+1/401+1/402+...+1/650= summation of 1/k going from 400 to 650. I know it is a harmonic...

Evaluate 1/400+1/401+1/402+...+1/650= summation of 1/k going from 400 to 650. I know it is a harmonic sum but how would I proceed to calculate?

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Answer #1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

Sum can be written as

650 650 399 に400 k=1 k=1

So, we know

Hn=ln(n)+0.5772156649

So,

H(650)=log(650)+0.5772156649----------eq1

H(399)=log(399)+0.5772156649---------eq2

Subtract eq1 and 2

So, The sum is log(650/399)~0.4880

Kindly revert for any queries

Thanks.

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