We are asked to evaluate the summation of 25 times 0.3 to the n plus 1 power, from n equals 2 to 10. In this case, we use a calculator with summation powers so as to accurately get the answer. Using a calculator, the asnwer is equal to 0.9643. 


You are watching: Evaluate the summation of 25 times 0.3 to the n plus 1 power, from n equals 2 to 10.


Step-by-step explanation:

We have to evaluate the expression:

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i.e. it could also be written as:

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i.e. we need to evaluate:

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Hence, this could be written as:

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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:

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Here a=1 and r=0.3

Hence the sum of geometric series is:

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Hence, the final evaluation is:

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Hence,



Answer from: cassi35
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alissa3329

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

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