what is the sum of the geometric series 15 E x=0 2(1/2)^x........... this is summation notation here..!!

Question

what is the sum of the geometric series    15 E x=0  2(1/2)^x...........  this is summation notation here..!!

driftracer305 · Answer

@ganeshie8

driftracer305 · Answer

@jim_thompson5910

driftracer305 · Answer

@Luigi0210

driftracer305 · Answer

@mathstudent55 ............sum help would be great....

campbell_st · Answer

well find the first few terms 

x = 0    2

x = 1    1

x = 2    1/2

x =  3   1/4

so the 1st term is 2, the common ratio is r = 1/2 and the number of terms is n = 16

since you are going from 0 to 15

so use the formula 

$$S_{n} = \frac{a(1 - r^n)}{(1 - r)}$$

hope it helps

dls · Answer

right^

driftracer305 · Answer

@campbell_st ........thanks a TON.......... just had some doubts.....

driftracer305 · Answer

k thx.... appreciate it

dls · Answer

$$\Huge \sum_{0}^{15} \frac{2}{2^x}= 2+ 1 + \frac{1}{2} + \frac{1}{4}....$$
3+ (sum of a GP)

dls · Answer

$$\Huge S_n = \frac{a(1- r^n)}{1-r}$$
where a is your first term and r the common difference

driftracer305 · Answer

should be  4  right...?

dls · Answer

$$\LARGE 3+\frac{\frac{1}{2} ( 1- \frac{1}{2^{14}})}{\frac{1}{2}}$$
this should be your answer I guess

driftracer305 · Answer

yup... it;s  4......... thanks a lot @DLS

dls · Answer

yeah one..because $$\LARGE \frac{1}{2^{14}} ->0$$ since its a very large quantity :)