Question

If an=1, for all positive integers n, what is the value of Sn, the nth partial sum of the infinite series ∑n=1∞an

Answer 1

The sum, written out, looks like

1 + 1 + 1 + …

So the first partial sum is 1, the second partial sum is 1+1 = 2, the third partial sum is 1+1+1 = 3, and so on. Therefore the nth partial sum is n.

Answer 2

The value of Sn, the nth partial sum of the provided infinite series ∑n=1∞an in which an=1, for all positive integers n is n.

What do you mean by infinite series?

The infinite series is the sum of addition of a sequence in which the number of terms present are infinite.

$a_1+a_2+a_3.....+a_n$

Here, ($a_n$) is the nth term of the sequence.

The value of nth term for all positive integers n is,

$a_n=1$

The sequence is,

$(a_n)_n=1,2,3....$

The infinite series given as,

$\sum_{n=1}^{\infty}a_n$

The nth partial sum of this series is,

$s_n=a_1+a_2+a_3+....+a_n\\s_n=a_1+a_2+a_3....a_{n-1}{+a_n\\s_n=(n-1)+n\\s_n=n$

Thus, the value of Sn, the nth partial sum of the provided infinite series ∑n=1∞an in which an=1, for all positive integers n is n.

Learn more about the infinite series here;

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