Fin the sum of the infinite geometric series if it exists 2

Fin the sum of the infinite geometric series, if it exists. 2 + 2/5 + 2/25 + 2/125+.... 5/2 2/5 12/5 does not exist use the Binomial Theorem to expand and express the result in simplifies form. Write the first three terms in the binomial expansion, expressing the result in simplified form. (x + 5)^20

Solution

15) This is an infinite geometric series with a = 2 and r = 1/5. Since | r | < 1, I can use the formula for summing infinite geometric series

Sum = a/(1 - r) = 2/(1 – 1/5) = 5/2 (option A)

16) (x – 5y)^5 = x⁵ 25x⁴y + 250x³y² 1250x²y³ + 3125xy⁴ 3125y⁵ (option B)

17) (x + 5)^20 = x²⁰ + 100x¹⁹ + 4750x¹⁸ (Option A)