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Question Number 122859 by mnjuly1970 last updated on 20/Nov/20
$... calculus(II)− analysis(I)... ::: consider the sequence {c_n }_(n=1) ^∞ in which :: c_n =1+(1/2)+(1/3)+...+(1/n) −ln(n) prove that the above sequence is convergent and then find its limit.$
$. . . c a l c u l u s (I I) - a n a l y s i s (I) . . .$ $::: c o n s i d e r t h e s e q u e n c e {c_{n}}_{n = 1}^{\infty}$ $i n w h i c h :: c_{n} = 1 + \frac{1}{2} + \frac{1}{3} + . . . + \frac{1}{n} - l n (n)$ $p r o v e t h a t t h e a b o v e s e q u e n c e i s$ $c o n v e r g e n t a n d t h e n$ $f i n d i t s l i m i t .$
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