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1 +(1)/(4) +(1.3)/(4.8)+(1.3.5)/(4.8.12)+… isequalto |
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Answer» `SQRT2` `(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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