AP EAMCET202421 May 2024Evening ShiftMathematicsLimitsActual

_ x 1 ( x+x^2+x^3+ +x^n-n x-1 )=

Options

An(n+1) 2
Bn+1 2
C2 n
Dn

Correct answer

A. n(n+1) 2

Step-by-step solution

aligned & _ x 1 ( x+x^2+x^3 . x^4-n (x-1) ) & = _ x 1 ( (x-1)+ (x^2-1 )+ (x^3-1 ) + (x^n-1 ) (x-1) ) & = _ x 1 (1+2 x+3 x^2+4 x^3 . . . n x^ n-1 ) & =1+2+3+4+ . . h= n(n+1) 2 . aligned

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