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:

Hence,

step-by-step explanation:

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