You are watching: Evaluate the summation of 25 times 0.3 to the n plus 1 power, from n equals 2 to 10.
We have to evaluate the expression:
i.e. it could also be written as:
i.e. we need to evaluate:
Hence, this could be written as:
Now, the series inside the parenthesis is a geometric series with first term as 1 and common ration as 0.3.
Hence, we could apply the summation of finite geometric series and get the answer.
We know that the sum of geometric series with n terms and common ratio less than 1 is calculated as:
Here a=1 and r=0.3
Hence the sum of geometric series is:
Hence, the final evaluation is:
Answer from: cassi35
a1=25(0.3)^2, common ratio = 0.3
So sum of first n terms of a geometric series = a1(1-r^n)/(1-r)
So sum of frist 10 terms of the given series = 25(0.3)^2(1-0.3^10)/ (1-0.3)
So sum of n=2 to n=10 is : 25(0.3)^2(1=0.3^10)/(1-0.3) -25(0.3)^2= 0.96426673425
Ask an expert a question
Pick a subjectMathematicsHistoryEnglishBiologyChemistryPhysicsSocial StudiesAdvanced Placement (AP)SATGeographyHealthArtsBusinessComputers and TechnologyFrenchGermanSpanishWorld Languages
View a few ads and unblock the answer on the site
See more: Can You Take Aleve And Benadryl Together, Aleve Nighttime