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c2 geometric series

Please help me with part b of this question

I am confused please explain to me in simple terms how the solution to part b. I looked at the solution bank for c2 edexcel and didnt understand it

thank you very much for helping
i have attached th question and the solution bank's answer

Attachment not found

The sum of the geometric series is not the same as the total distance travelled. As shown in the solution, you have to add heights other than the first one, 10, twice since the ball travels up then back down between each bounce. But multiplying the series sum you have by two also adds the 10 twice, you don't want that so have to subtract it.