Show that if Deduce that Show that if |r| n a/(1 r) 2 as n

Question:

Show that if

T= a + 2ar + 3ar + 4ar+...+ nar-1 then (1r)T, = a +ar+ar+...+ar"- - nar

Deduce that

T = a(1-r") (1-r) nar" 1-r

Show that if |r| n → a/(1 – r)2 as n → ∞. Hence sum the infinite series

- 1+ 3/3 + 1/3 + 27 5 + + 81 + k 3k-1 +.

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