1. Prove that 1 + r + r 2 + … + r n = (1 – r n + 1 )/(1 – r) for all n ∈ N, when r ≠ 1. 2. Prove that  +  + +….+ =  for all n ∈ N. 3. Prove that XXXXXXXXXX 2 + … + 2 n – 1 = 2 n – 1, for all n ∈ .


1. Prove that 1 + r + r2
+ … + rn
= (1 – rn + 1)/(1 – r) for all n ∈ N, when r ≠ 1.


2. Prove that



 +
 +
+….+
=
 for all n ∈ N.


3. Prove that 1 + 2 + 22
+ … + 2n – 1
= 2n
– 1, for all n ∈
.



May 05, 2022
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