...formed by some regular law, and the number of the terms is unlimited, is called an infinite series. 554. An infinite series is said to be convergent when the sum of the first n terms cannot numerically exceed some finite quantity however great n may be. 555. An infinite series is said...

...formed by some regular law, and the number of the terms is unlimited, is called an inßnite teñes. 554. An infinite series is said to be convergent when the sum of the first n terms cannot numerically exceed some finite quantity however great n may be. 555. An infinite series is said...

...general, are examples of finite series ; but, in Art. 380, we considered infinite Geometrical series. 409. An infinite series is said to be convergent when the sum of the first n terms cannot numerically exceed some finite quantity, however large n may be ; and it is said to be divergent...

...number of terms is limited. An Infinite series is one of which the number of terms is unlimited. 257. An infinite series is said to be Convergent when the sum of the first n terms approaches a limit as n is increased indefinitely ; and the limit is called the Sum of the infinite series. If the...

...developed by other methods, one of the most important of which will be considered in Chapter XXXII. 450. A series is said to be convergent when the sum of the first n terms approaches a certain fixed quantity as a limit (Art. 209), when n is indefinitely increased; this limiting value...

...the sum either tends to become equal to a certain finite limit, or else it becomes infinitely great. An infinite series is said to be convergent when the sum of the first n terms cannot numerically exceed some finite quantity however great n may be. An infinite series is said to...

...£ ; and so on. The successive approximate sums approach, but never reach, the finite value 2. 325. An infinite series is said to be convergent when the sum of the terms, as the number of terms is indefinitely increased, approaches some fixed finite value; this finite...

...1|-^; and so on. The successive approximate sums approach, but never reach, the finite value 2. 360. An infinite series is said to be convergent when the sum of the terms, as the number of terms is indefinitely increased, approaches some fixed finite value; this finite...

...infinite ; hence no value of x is admissible which will render the infinite series M infinite in value. An infinite series is said to be convergent when the sum of the first n terms cannot numerically exceed some finite quantity, however great n may be. If by taking n large enough...

...examples of finite series. 2. In Arts. 167 and lo'8 we considered infinite geometrical series. 175. A series is said to be convergent when the sum of the first n terms cannot numerically exceed some assignable number, however great n m&y be. A series is said to be divergent...