(x+1)(x-2)(x+3)(x-4) ............ (x-100) = a0 + a1x + a2x^2 + ......
find the value of a1 ???
is the ansr 100!log 2 base e
i think the value of a1 wud be 50
i thnk ans = -50 instead of 50
can u take the trouble 2 xplain
To find a1 u'll look at the cofficients of 'x" only..i.e
(X-2X)(3X-4X)(4X-5X).................(99X-100X). & these would be 50 terms, so
we get a1 = (-1 x 50 )= -50..ans...
we have to look at the coefficient of x
this is found by taking x from one of the factors and constants from the rest and doing it in all possible ways.
the sum will be 100! (1-1/2+1/3-1/4+.....+1/100)
now 1-1/2+1/3-1/4+.....+1/100+... converges to ln2 , from Maclaurin's series.
hense the answer 100! ln2
..
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i think the value of a1 wud be 50
i thnk ans = -50 instead of 50
can u take the trouble 2 xplain
To find a1 u'll look at the cofficients of 'x" only..i.e
(X-2X)(3X-4X)(4X-5X).................(99X-100X). & these would be 50 terms, so
we get a1 = (-1 x 50 )= -50..ans...
we have to look at the coefficient of x
this is found by taking x from one of the factors and constants from the rest and doing it in all possible ways.
the sum will be 100! (1-1/2+1/3-1/4+.....+1/100)
now 1-1/2+1/3-1/4+.....+1/100+... converges to ln2 , from Maclaurin's series.
hense the answer 100! ln2
..
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