3. By using mathematical induction proves 2' + 22 + 2 +.. +2" = 2"*! – 2 is true for all positive 3 2n integers n. Hence find 2" r=n

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Q: 10. Use induction to show that 1x2 + 2x3 + + n(n+1) = " for all n € N.

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A: Note: As you posted multiple questions I need to solve only the first question i.e. question 5.

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Q: Mathematical Induction.

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Q: n —(2) - (-) (1)¹(1)(). (n-1)

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Q: 8. Prove 1² +2²+3² + + n² = n(n+1)(2n+1) 6 is TRUE using mathematical induction

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