Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Let n be a positive integer. Using school level methods, show that 1+1/22 + 1/32

ID: 3099023 • Letter: L

Question

Let n be a positive integer. Using school level methods, show that
1+1/22 + 1/32 + ..... + 1/n2 < 1.7. (Euler showed that the infinite sum 1+1/22 + 1/32 + ..... + 1/n2 is equal to p/6, but I know of no high school level proof.) Hint: Approximate the " tail" (the sum from 1=(k + 1)2 on, for suitable k), by something easily summed. Let n be a positive integer. Using school level methods, show that
1+1/22 + 1/32 + ..... + 1/n2 < 1.7. (Euler showed that the infinite sum 1+1/22 + 1/32 + ..... + 1/n2 is equal to p/6, but I know of no high school level proof.) Hint: Approximate the " tail" (the sum from 1=(k + 1)2 on, for suitable k), by something easily summed.

Explanation / Answer

soo lOng! xp