Help to use mathematical induction to prove that the square of 1 / 2 + 1 / 3 is always less than 1 when it is added to the square of 1 / n Notice that it's 1 / 2!

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• 1. 1 = 1 square 1 + 3 = 2 square 1 + 3 + 5 = 3 square How to do it? Help ～
• 2. 2. (3 √ 5 + 2 √ 6) (2 √ 6-3 √ 5) 3.√2（√2-√6）+（1+√3）（1-√3） 4.（2√3-3√2）（2√2+√3）
• 3. (√ 5 + 1) (√ 5-1) = (2 - √ 7) (√ 7 + 2) = (2 √ 3 + 1) square (7 - √ 3) (2 √ 3 + 1)= (√ 5 + 1) (√ 5-1) = (2 - √ 7) (√ 7 + 2) = (2 √ 3 + 1) square =? （7-√3)(2√3+1)=
• 4. Square of - 5 + 2 × (- 3) square - 7 × (- 1 / 3) square=
• 5. Calculation: 12-22 + 32-42 + 52-62 + +20012-20022+20032-20042．______
• 6. The square of 1 - the square of 2 + the square of 3 - the square of 4 + the square of 5 - the square of 6 + +The square of 99
• 7. Calculation: (- 4 square + 6) × (1 / 5-3 / 2)
• 8. The formula of finding the sum of the first n terms in the equal ratio sequence
• 9. By using the first n terms of the equal ratio sequence and the formula, it is proved that: a^n+a^n-1*b+a^n-2*b^2+… +b^n=a^n+1-b^n+1/a-b
• 10. What is the formula of the sum of the first n terms of an equal ratio sequence?
• 11. Why 1 + 3 + +What about the square of (2n-5) + (2n-3) = (n-1)?
• 12. 1 + 3 + 5 + 7 +. + (2n-1) = the square of n Is this formula right?
• 13. Proof: inequality 2 / 2 + 3 / 2 + 4 / 2 + n / 2 is less than N / 1 No mistakes... This is from a book. It seems to be less than N-1 of n
• 14. 1,5,9,13,17 the rule of the above group of numbers is: write the formula
• 15. How to fill in the formula of 1 + 2 + 3 + 2 + 1 according to the rule
• 16. 1, 3, 7, 13
• 17. A formula for finding a group of number rules in high school mathematics
• 18. 5 / 4, 29 / 9, 83 / 16, 180 / 25, 331 / 366 find the general formula of this group of numbers or tell the law of this group of numbers The last number is 331 / 36. If you are interested, I will give you a bonus
• 19. How much is the next? It's better to have a general formula! 32144680, the following numbers are required
• 20. General term formula of a group of numbers The general formula of two groups of numbers is 3,8,15,24,35, two negative 2 / 3,4 / 15, negative 6 / 35,8 / 63, negative 10 / 99 ～