## anonymous one year ago help please! Evaluate the summation of 20 times 0.5 to the n minus 1 power, from n equals 3 to 12.. 9.99 19.95 29.98 39.96

1. anonymous

$\sum_{n=3}^{12} 20 \times 0.5^{n-1}$ This is it, right?

2. anonymous

yes

3. anonymous

@larryboxaplenty

4. anonymous

I can't help you right now, sorry, g2g for a sec someone else can help. I know the answer for forget the shortcut

5. anonymous

6. anonymous

$\large 20 \cdot \left(0.5^{n-1}\right)$ start with plugging in $$n=3$$ and work your way up to $$n=12$$ by adding all the values.

7. anonymous

$\large 20\cdot (0.5^{3-1} + 0.5^{4-1}+0.5^{5-1}+...+0.5^{12-1})$

8. welshfella

or you can use the formula for the sum of a geometric series Sn = a . (1 - r^n) ------ 1 - r

9. welshfella

here a = 20*0.5^2 , n = 11 and r = 0.5

10. anonymous

so would i get 9.99 as the answer

11. anonymous

@welshfella

12. welshfella

yes

13. anonymous

thank you

14. welshfella

yw