1. Prove that 1 2 + 2 2 +…… +n 2 = n(n +1)(2n +1) for all n ∈ N. 2. Prove that 1 3 + 2 3 +…… +n 3 = n 2 (n +1) 2 for all n ∈ N. 3. Prove that 1 3 + 2 3 +…… +n 3 = (1+2+….+n) 2 for all n ∈ N. 4. Prove...


1. Prove that 12
+ 22+…… +n2
=
n(n +1)(2n +1) for all n ∈ N.


2. Prove that 13
+ 23+…… +n3
=
n2(n +1)2
for all n ∈ N.


3. Prove that 13
+ 23+…… +n3
= (1+2+….+n)2
for all n ∈ N.


4. Prove that



 +
 +
 +…….+
 =
, for all n.



May 05, 2022
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