math

(1-1/2^2 )(1-1/3^2 )(1-1/4^2 )…(1-1/2011^2 )

  1. 👍 0
  2. 👎 0
  3. 👁 118
  1. (1-1/2^2)(1-1/3^2)...(1-1/n^2)
    =(2^2-1)/2^2 * (3^2-1)/3^2 * ...(n^2-1)/n^2
    =(2+1)(2-1)/2^2 * (3+1)(3-1)/3^2 *... (n+1)(n-1)/n^2
    =(2+1)(3+1)...(n+1) * (2-1)(3-1)...(n-1)/(1*2*3...n)^2
    =((n+1)!/2)(n-1)!/(n!)^2
    =(1/2)[(n+1)/(n)] n!*n!/(n1)^2
    =(n+1)/(2n)

    Therefore

    Π(1-1/i^2) i=2 to n
    =(n+1)/(2n)

    For n=2011,
    Π(1-1/i^2) i=2 to 2011
    =(2011+1)/(2*2011)
    =2012/4022

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 5 of 90 lotto equation formula

    Example: on 5 Feb. 2011, draws were::: 44 – 68 – 90 – 64 – 66 and 12 Feb. 2011, draws were::: 89 – 27 – 12 – 49 – 40 Each draw has a corresponding machine number. For instance, the machine numbers for the 5 Feb.

  2. MATH

    Hyabuza Japanese Restaurant received an invoice, dated February 20, 2011, for supplies they ordered that had a list price of $2,700 from a supplier that offered a series discount of 15/8/4 and carried terms of 3/10, 1/15, N/30.

  3. Statistics

    From these past lotto results. 12/05/2011(31-25-36-48-9). 19/05/2011(16-81-59-84-76). 26/05/2011(19-2-57-69-36). Can anyone predict todays winning numbers? It's a 5/90 lotto

  4. Math

    The following table shows the profit, in millions of dollars, for a company from 2010 to 2013. 2011 24 Million 2011 neg 354 Million 2012 248 Million 2013 587 Million How much more profit did the company make in 2010 than in 2011,

  1. Financial Accounting

    Prepare adjusting journal entries for the year ended December 31, 2011 for each of the independent situation in (a) to (f). Assume that prepaid expenses are initially recorded in asset accounts. Assume that fees collected in

  2. accounting

    using the following information, calculate inventory turnover ratio, the average days in inventory, and the gross profit ratio for Howard Company for the year ended december 31, 2011( round to two decimal places) sales $225,00

  3. computers/it

    2011-07-15 18:30:34: DB Settings - ORACLE_HOME was located and set to E:\ORACLE\ORA92 2011-07-15 18:31:04: Failed to connect to DBSettings Service instance 2011-07-15 18:31:04: Failed to connect to the settings service, aborting

  4. accounting

    O' Hara Company began operations on December 1, 2011. Presented below is selected information related to O' Hara Company at December 31, 2011. Office Equipment ₤ 40,000 Utilities Expense ₤ 6,000 Cash 14,000 Accounts Receivable

  1. Accounting

    O' Hara Company began operations on December 1, 2011. Presented below is selected information related to O' Hara Company at December 31, 2011. Office Equipment ₤ 40,000; Utilities Expense ₤ 6,000; Cash 14,000; Accounts

  2. Accounting

    O' Hara Company began operations on December 1, 2011. Presented below is selected information related to O' Hara Company at December 31, 2011. Office Equipment ₤ 40,000; Utilities Expense ₤ 6,000; Cash 14,000; Accounts

  3. Civics ASAP PLZ =:)

    In 2002, one U.S. dollar could be exchanged for 133 Japanese yen, and in 2011, a U.S. dollar was worth 77 yen. Based on this information, which statement is definitely true? Demand for the yen increased between 2002 and 2011 and

  4. accounting

    Pike Corporation paid $100,000 for a 10% interest in Salmon Corp. on January 1, 2010, when Salmon's stockholders' equity consisted of $800,000 of $10 par value common stock and $200,000 retained earnings. On December 31, 2011,

You can view more similar questions or ask a new question.