Question

The sum of the first ten terms 1, 3/2, 7/4, 15/8, ...

Answer 1

The given series terms can be described as follows:

`\begin{gathered} A_1=1 \\ A_2=(3)/(2) \\ A_3=(7)/(4) \\ A_4=(15)/(8) \\ \ldots \\ A_n=(2^n-1)/(2^(n-1)) \end{gathered}`

From this, we are able to calculate and sum the rest of the terms until A10, as follows:

`\begin{gathered} A_5=(31)/(16) \\ A_6=(63)/(32) \\ A_7=(127)/(64) \\ A_8=(255)/(128) \\ A_9=(511)/(256) \\ A_(10)=(1023)/(512) \\ \\ S=\sum ^(10)_(n\mathop=1)A_n=(9217)/(512) \end{gathered}`

From the solution de developed above, we are able to conclude that the answer to the present question is:

`S=(9217)/(512)`