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Publish On: 2019-03-16

ally

Total Post: 571

Question: Explain infinite series

Reply On: 2013-10-08

Mjay Jollay

Total Post: 0

ANS: Explain infinite series

Let < un > be real sequence. Then the expression of the form u1 + u2 + u3 + …. + un + …. is called an infinite series and is symbolically expressed as  or simply Σ un. The real numbers u1, u2, u3, …. , un … , are known as the first, second, third …. nth term ….. respectively of the infinite series. The nth term of the infinite series  is also called as the greater term.

Now, <un> is a real sequence.

The terms of the sequence, viz. u1, u2, u3, …. , un …. , are arranged and formed according to some definite law.

∴ In the light of this, an infinite series can be defined as the succession of terms which are formed according to some definite law,

e.g. 1 + ½ + 1/3 + ¼ + …. + 1/n + ….

or simply  is an infinite series.
 

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