Use principle of Mathematical Induction to prove that:
11∗ 2 + 12∗3 + …………..+ 1𝑛(𝑛+1) = 𝑛𝑛+1

We are tasked with proving the statement

\[
11 \cdot 2 + 12 \cdot 3 + \dots + 1n(n + 1) = \frac{n}{n + 1}
\]

using the principle of mathematical induction.

### Step 1: **Base Case (n = 1)**

For \(n = 1\), the left-hand side (LHS) of the equation is:

\[
11 \cdot 2 = 2
\]

The right-hand side (RHS) of the equation is:

\[
\frac{1}{1 + 1} = \frac{1}{2}
\]

Clearly, \(2 \neq \frac{1}{2}\), so the given equation does not hold when \(n = 1\).

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Use principle of Mathematical Induction to prove that: 11∗ 2 + 12∗3 + …………..+ 1𝑛(𝑛+1) = 𝑛𝑛+1

This article provides a step-by-step explanation of how to use the principle of mathematical induction to prove a summation formula involving terms like 1n(n+1). It discusses both the base case and inductive step, aimed at high school students in Grades 10-12.

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