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Let S_n= _ x=1 ^n x ! ; n 6, T= ( (S_n-7 [ S_n 7 ] ) ) . If ₀^1 T 1-x^2 d x= a b - ^c where a, b, c W ; b 0 , then find ( b c +a ) .

Correct answer

6

Step-by-step solution

aligned & S_n=1 !+2 !+3 !+4 !+5 !+6 !+7 !+ & S_n=1+2+6+24+120+720+7 I aligned S_n=873+71 ...(1) array r S_n 7 = 873 7 +I [ S_n 7 ]=124+I array 7 [ S_n 7 ]=868+7 I ...(2) aligned & Eqn. (1) - Eqn. (2) =5 & T= ⁻¹( 5)=5-2 & ₀^1 5-2 1-x^2 d x= (5-2 ) 2 = 5 2 - ^2 & ( b c +a )= 2 2 +5=6 & aligned

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