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 that1+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.
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soo lOng! xp
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