Find the sum
a1 = 625, n= 5, r = 3/5
a1 = 80, n= 7, r = - 1/2
a1 = 343, an = -1, r = -1/7
@campbell_st @robtobey

Question

Find the sum
a1 = 625, n= 5, r = 3/5
a1 = 80, n= 7, r = - 1/2
a1 = 343, an = -1, r = -1/7
@campbell_st @robtobey

campbell_st · Answer

ok... so these are all geometric series... where the common ratio is between 

-1 < r < 1

this means that each series had a limiting sum.... 

which is found using 

$$S_{\infty} = \frac{a_{1}}{1 - r}$$

just substitute and evaluate

the alternate method , given you have  a value for n, the number of terms is 

$$S_{n} = \frac{a_{1}(1 - r^n)}{1 - r}$$

just substitute and calculate

hope it helps