Find the sum of the following series.Round to the nearest hundredth if necessary. 2+12+72+ldots +120932352 Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^n)/(1-r)

Question

Answer 1

To find the sum of the given series, we need to identify the first term, common ratio, and the number of terms in the series.The first term

is 2.The common ratio

can be found by dividing the second term by the first term:

Next, we need to determine the number of terms

in the series. We know the last term is 120932352. The

-th term of a geometric series is given by:

So, we set up the equation:

Solving for

:

Taking the logarithm of both sides:

Using a calculator to find the logarithm:

Since

must be an integer, we round to the nearest whole number:

Now, we can use the formula for the sum of a finite geometric series:

Substituting the values:

Calculating the numerator:

Now, the denominator:

So, the sum is:

Therefore, the sum of the series is:

Problemas