Find the sum of the series S8 for the series 10 – 5 + 2.5 – 1.25 + . .

sum-of-the-series-s8
10-5-25-125-2

#1

Find the sum of the series S8 for the series 10 – 5 + 2.5 – 1.25 + . . .

Answer:

lets say -5=a1 2.5=a2 -1.25=a3
then series is :
a1 + ((a1)^2)/10) + ((a1)^3)/10^2) + …
it can be written as:
a1 (1 + ((a1)/10) + ((a1)^2/10^2) +…
then
a1 (1 + (a1/10) + (a1/10)^2 + …
now we can apply the summation formula which is
Sn = ( (1 - (r^n)) / (1 - r) ) x a1
for this series r=a1/10 , a1=-5 and n=7 (because there is one element outside which is 10)
then
S7 = -3.36
S8 = 10 + (-3.36) = 6.64