- #1

GreenPrint

- 1,196

- 0

## Homework Statement

Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than 10^-5. Although you do not need it, the exact value of the series is given.

ln(128) = 7*sum[k=1,inf] of (-1)^(k+1)/k

## Homework Equations

**3. The Attempt at a Solution [/b**

| ln(128) - 7*sum[k=1,n] of (-1)^(k+1)/k | < 1/10,000

subtracted ln(128) from both sides

|-7*sum[k=1,n] of (-1)^(k+1)/k | < 1/10,000 - ln(128)

simplified the negative on the left hand side and absolute value

7*sum[k=1,n] of 1/k < 1/10,000 - ln(128)

divided through by 7

sum[k=1,n] of 1/k < 1/70,000 - ln(128)/7

I'm unsure were to go from here, thank you for any help you can provide me.

| ln(128) - 7*sum[k=1,n] of (-1)^(k+1)/k | < 1/10,000

subtracted ln(128) from both sides

|-7*sum[k=1,n] of (-1)^(k+1)/k | < 1/10,000 - ln(128)

simplified the negative on the left hand side and absolute value

7*sum[k=1,n] of 1/k < 1/10,000 - ln(128)

divided through by 7

sum[k=1,n] of 1/k < 1/70,000 - ln(128)/7

I'm unsure were to go from here, thank you for any help you can provide me.