Find a formula for 1 1 1 1⋅ 2 + 2⋅ 3 +⋯ + n(n +1) by examining the values of this expression for small values of n. b) Prove the formula you conjectured in part (a).
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Step 1: Understand the problem We want to find a formula for the sum: \[ S_n = 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \cdots + n(n+1) \] Show more…
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5. a) Find a formula by examining the values of this expression for small values of n. b) Prove the formula you conjectured in part (a)
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In Problems $47-50,$ suggest a formula for each expression, and prove your conjecture using mathematical induction, $n \in N$. $$ \frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4}+\cdots+\frac{1}{n(n+1)} $$
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Find a formula for 1/(1*2) + 1/(2*3) + ... + 1/(n*(n+1)) by examining the values of this expression for small values of n. Then prove that your formula is correct.
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