Find the sum of the following geometric progressions : (a2 - b2), (a-b

1.	Find the sum of the following geometric progressions : (a2 - b2), (a-b), \((\frac{a-b}{a+b})\),........ to n terms
Answer» Common Ratio = r = \(\frac{(a^2 - b^2)}{(a-b)}\) = \(\frac{(a+b)(a-b)}{(a-b)}\) = a+ b ∴ Sum of GP for n terms = \(\frac{a(r^n-1)}{r-1}\) ...... (1) ⇒ a = (a² - b²), r = (a + b), n = n ∴ Substituting the above values in (1) we get ⇒ \(\frac{(a^2-b^2)((a+b)^n-1)}{a+b-1}\)

Find the sum of the following geometric progressions : (a2 - b2), (a-b), \((\frac{a-b}{a+b})\),........ to n terms

Answer»

Common Ratio = r = \(\frac{(a^2 - b^2)}{(a-b)}\) = \(\frac{(a+b)(a-b)}{(a-b)}\) = a+ b

∴ Sum of GP for n terms = \(\frac{a(r^n-1)}{r-1}\) ...... (1)

⇒ a = (a² - b²), r = (a + b), n = n

∴ Substituting the above values in (1) we get

⇒ \(\frac{(a^2-b^2)((a+b)^n-1)}{a+b-1}\)