# If Σ an is divergent and Σ bn is convergent, show that Σ (an – bn) is divergent . infinite series problems with solution solved problems in calculus

Solution –

## Assume \sum (a_n-b_n) is convergent. Then, \sum a_n=\sum b_n+\sum (a_n-b_n) is convergent, contrary to hypothesis

Q-Find the values of x for which the series Inx + (Inx)^2 + (Inx)^3 + • • • converges and express the sum as a function of x

## Solution

lnx+(lnx)^2+(lnx)^3+(lnx)^4+...

## The geometric sum formula for infinite terms is given as:

If common ration |r| < 1, S_\infty=\frac{a}{1-r}

## If |r| > 1, the series does not converge and it has no sum.

Where