1.

1 +(1)/(4) +(1.3)/(4.8)+(1.3.5)/(4.8.12)+… isequalto

Answer»

`SQRT2`
`(1)/(sqrt2) `
`sqrt3 `
`(1)/(sqrt3)`

Solution : ` 1 +(1)/(4)+(1.3)/(4.8)+ (1.3.5)/(4.8.12) + … `
`(1 +X ) ^n =1+nx+(n (n- 1 ))/(2!)x^ 2`
` + (n(n - 1 )(n - 2 ))/(3!)x ^ 3+… `
On comparingtheaboveexpansion, we get,
`thereforenx = (1)/(4) ""`...(1)
` (n(n - 1 ))/(2!) x ^ 2 = (1.3)/(4.8) ""`...(2)
` (n (n - 1 )(n -2))/(3!)x ^ 3=(1.3.5 ) /(4.8.12)"" `...(3)
(2) `div`(1)
`((n-1))/(2)x = (3)/(2XX 4 )`
`(n - 1 )x =(3)/(4) "" `...(4)
From(3)` div `(2)
` ((n-2))/(3)x =(5)/(3)XX (1)/(4)""`...(5)
From(4)and(5) , `x =( - 1 ) /(2), n =( - 1 ) /(2) `
`therefore1 +(1)/(4)+(1.3)/(4.8)+ (1.3.5 )/(4.8.12)+... = (1 -(1)/(2) ) ^( -1/2)`
`= ((1)/(2))^( -1/2)= sqrt2 `


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