Discrete math

Question

Let $w \in \sum$$*$ be a string, with $\sum$ being the alphabet. Let $w^R$ be the reversal of string $w$, using induction prove that $(w^R)(w^R). . .(\text{for k times}) = (ww . . .(\text{for k times}))^R.$

Comments

For length 1 string w = a

(a^R)(a^R)...(for k times)=(aa...(for k times))^R

For length 2 string w = ab

(ab^R)(ab^R)...(for k times)=(abab...(for k times))^R

babababababab..ba = babababababa..ba

so for string for length k  

(w^R)(w^R)...(for k times)=(ww...(for k times))^R

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@debashish..can you pls give any good links to see such proofs for discrete maths questions?