Answer:
A.The summation of 940 times one fifth to the i minus 1 power ,from i equals to infinityb .'the sum is 1,175.
Step-by-step explanation:
We are given that the population of a local species of flies can be found using an infinite geometric series
Where [tex]a_1=940,common\; ratio,r=\frac{1}{5}[/tex]
We know that the formula of sum of infinite G.P
[tex]\sum_{1}^{\infty}ar^{n-1}=\frac{a}{1-r} [/tex]because r<1
Where a= First term of GP
r=Common ratio
Substituting the values then we get
Population=[tex]\sum_{1}^{\infty}940(\frac{1}{5})^{i-1}=[/tex]
[tex]\sum_{1}^{\infty}940(\frac{1}{5})^{i-1}=\frac{940}{1-\frac{1}{5}}[/tex] r <1
[tex]\sum_{1}^{\infty}940(\frac{1}{5})^{i-1}[/tex]
=[tex]\frac{940}{\frac{5-1}{5}}[/tex]
=[tex]\frac{940}{\frac{4}{5}}[/tex]
=[tex]\frac{940\times 5}{4}[/tex]
=[tex]235\times 5[/tex]
Population=[tex]\sum_{1}^{\infty}940(\frac{1}{5})^{i-1}[/tex]=1,175
Hence, the sum is 1,175
Hence, option A is true.
Answer : A.The summation of 940 times one fifth to the i minus 1 power ,from i equals to infinityb .'the sum is 1,175.
