Question

What is the sum of the following series-
6 - 3 + 3/2- 3/4.... till 15 terms?

Answer 1

can u determine the common ratio of this geometric sequence??

Answer 2

The ratio is -1/2 I guess.

Answer 3

yes its correct -1/2 :)
so this is your 'r'
the 1st term a=6
and the formula for 'n'(here n=15) terms is
a(1-r^n)/(1-r)
can u put the values and find the sum now??

Answer 4

I tried, but the answer is not coming out to be correct! :/

Answer 5

whats the answer given?
i am getting it with that formula as (1+2^15)/2^13....did u get the same?

Answer 6

Answer is given to be 4.000 :/
And no, I did not get that!

Answer 7

(1+2^15)/2^13 is actually 4.00012207 so try again to substitute values in that formula to get (1+2^15)/2^13.....if u don't get i will show my steps afterwards...

Answer 8

Okay! Thank you soo much! I am trying now, I'll let you know if I get the answer. :D

Answer 9

Hey! I am sorry, but how did you get that? I have been stuck on this since 2 hours and I still didn't get that answer :/

Answer 10

\[\frac{a(1-r^n)}{(1-r)}= \frac{6* (1-(-1/2)^{15})}{1-(-1/2)}\]
\[4(1+ \frac{1}{2^{15}})\]
\[2^2(1+\frac{1}{2^{15}})\]
\[\frac{1+2^{15}}{2^{13}}\]
now tell which step u did not reach...

Answer 11

Haha, I didn't reach the second one.

Answer 12

now could u or should i show how i reached that step?

Answer 13

Please show me! I didn't understand.

Answer 14

\[\frac{6}{1-(-\frac{1}{2})}=\frac{6}{1+(\frac{1}{2})}=\frac{6}{\frac{3}{2}}=\frac{12}{3}=4\]

Answer 15

\[(1-(-1/2)^{15})=(1-(-1)^{15}/2^{15})=(1+\frac{1}{2^{15}})\]
now which step??

Answer 16

I got it, I got it!!! :D Thank youuu soo much! I worked my way out. And I got the answer! THANKYOU! :D I owe you for spoon feeding me through the question! :D

Answer 17

your welcome :) and u don't owe me anything....i am happy to help,so u made me happy :D

Answer 18

Thank you! This is my first time here, and you really helped me! :)