Question

Medal for help! Help with finding the general term for this series: −4/8+16/64−64/512+256/4096...

Answer 1

If you simplify each term it becomes: -1/2, +1/4, -1/8, +1/16, ....

Answer 2

so the general term is \[(-1)^{n}\times \frac{ 1 }{ 2^{n} }\]

Answer 3

The (-1)^n would be the alternating sign in the series?

Answer 4

yup when n is odd. it will become minus sign. and when n is even it will become + sign

Answer 5

so it will give alternate +,- sign as in your series

Answer 6

If you want the nth term WITHOUT simplification, then it is the above solution * (4/4)^n