Mathematics
Grade10
Easy

Question

What is the expansion of (x + y)1000?

  1.  sum from T equals 0 to T minus 10 of open parentheses 100 Cr to the power of 1000 minus tau end exponent y to the power of r close parentheses
  2.  sum from t equals 0 to r minus 1000 of open parentheses 100 Crx to the power of 1000 minus r end exponent y to the power of r close parentheses
  3.  sum from T equals 0 to tau equals 1000 of open parentheses 10 Cr to the power of 1000 minus tau end exponent y to the power of tau close parentheses
  4.  sum from r equals 0 to tau equals 10 of open parentheses 10 Cr to the power of 10 minus tau end exponent y to the power of tau close parentheses

The correct answer is: sum from t equals 0 to r minus 1000 of open parentheses 100 Crx to the power of 1000 minus r end exponent y to the power of r close parentheses


    The expansion can be done using the binomial theorem.
    (x + y)1000 = 1000C0 x1000 y0 + 1000C1 x999 y1 +….+ 1000C999 x1 y999 + 1000C1000 x0 y1000
    This can also be written as,

    (x + y)1000 =  sum from tau equals 0 to r equals 1000 of open parentheses 100 Crx to the power of 1000 minus tau end exponent y to the power of r close parentheses

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