Question
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers $n$.$$1^3+2^3+3^3+\cdots+n^3=\frac{1}{4} n^2(n+1)^2$$
Step 1
The left-hand side (LHS) of the equation is \( 1^3 = 1 \). The right-hand side (RHS) of the equation is \( \frac{1}{4} \times 1^2 \times (1+1)^2 = \frac{1}{4} \times 1 \times 4 = 1 \). Since LHS = RHS, the base case holds true. Show more…
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