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If this limit is not finite the sequence is called Divergent.

A series convergence calculator is used to find out the sum of the sequence and for determining convergence and divergence among series.

Illustration 1.

The sequence 1, 1/2,1/3……..1/n is convergent since a

Illustration 2.

The sequence 1, 2, 3, 4……n is divergent since a

Find the limit of sequence whose n

a

l→∞n

Solution

Lt

n→∞ n

Since in the problem its given Limit n→∞a

We will take ½ common from the numerator and ¼ common from the denominator.

Now we get,

Lt

n→∞ 1/4 (n

We know that 1+2+3+…n is equal to

2

common in the denominator so we get.

Lt ½*

n→∞ ___

n

Now we take the common factors and cancel them.

Lt

n→∞ 1+4/n+12/n

Since limit n →∞ we get,

1+4*0+12*0

Hence limit n→∞, anequals 1.