1.

For any two positive integers x and y f(x,y)=1/((x+1)!)+1/((x+2)!)+1/((x+3)!)+……..+1/((x+y)!), then which of the following options is/are correct

Answer»

`f(x,y) le 1/x (1/(x!)-1/((x+y)!))`
`lim_(y to OO)(f(x,y)) le 1/(x!)`
`f(x,x) lt 1/((x-1)!)`
`f(2,2)` is EQUAL to `2/3`

SOLUTION :`x/((x+i)!) le (x+i-1)/((x+i)!)=1/((x+i-1)!)-1/((x+i)!)`
`xsum_(i=1)^(y)1/((x+i)!) le 1/(x!)-1/((x+y)!)` …(1)
`lim_(y to oo) (f(x,y)) le 1/(XX!) le 1/(x!)`…….(2)
`f(x,x)=1/((x+1)!)+1/((x+2)!)+……….+1/((x+x)!) le x/(x!)=1/((x-1)!)`


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