Question

Prove that
samesang infinite n=1 (1)^n+1/n^2

Answer 1

Answer:

Series : Let (an) be a sequence of real numbers. Then an expression of the form a1 +a2 +a3 +......

denoted by P∞

n=1 an, is called a series.

Examples : 1. 1 + 1

2 +

1

3 + .... or P∞

n=1

1

n

2. 1 + 1

4 +

1

9 + .... or P∞

n=1

1

n2

Partial sums : Sn = a1 + a2 + a3 + ...... + an is called the nth partial sum of the series P∞

n=1 an,

Convergence or Divergence of P∞

n=1 an

If Sn → S for some S then we say that the series P∞

n=1 an converges to S. If (Sn) does not

converge then we say that the series P∞

n=1 an diverges.