## Solving problems in differential calculus: I, Part 2 |

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Page 75

(ii) 5B=l+i+i+^+---+^l since this is a geometric series with common ratio -i. As n -*

oo ... Hence Sn -» f, and the series is convergent. ... Show that the

-* S.

(ii) 5B=l+i+i+^+---+^l since this is a geometric series with common ratio -i. As n -*

oo ... Hence Sn -» f, and the series is convergent. ... Show that the

**harmonic****series**J] - is divergent. n If a series is convergent to sum S, then Sn -* S and S2n-* S.

Page 77

Leslie Maurice Brown. 19.4. Examine for convergence the series ... Further, 2 vn

is the

Hence £ un is divergent by the Comparison Test. (ip) Here un = n/(2n + l).

Leslie Maurice Brown. 19.4. Examine for convergence the series ... Further, 2 vn

is the

**harmonic series**with the first term omitted, and is consequently divergent.Hence £ un is divergent by the Comparison Test. (ip) Here un = n/(2n + l).

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