Nh+(n(n-1)h^2)/2........=? Please explain

Asked by ananya | 4th Oct, 2015, 11:23: AM

Expert Answer:

C o n s i d e r space t h e space B i n o m i a l space T h e o r e m space f o r space open parentheses 1 plus x close parentheses to the power of n colon open parentheses 1 plus x close parentheses to the power of n equals 1 plus fraction numerator n x over denominator 1 factorial end fraction plus fraction numerator n open parentheses n minus 1 close parentheses x squared over denominator 2 factorial end fraction plus fraction numerator n open parentheses n minus 1 close parentheses open parentheses n minus 2 close parentheses x cubed over denominator 3 factorial end fraction plus.... G i v e n space e x p r e s s i o n space i s space n h plus fraction numerator n open parentheses n minus 1 close parentheses h squared over denominator 2 end fraction plus... T h u s comma space f r o m space t h e space b i n o m i a l space e x p a n s i o n space o f space open parentheses 1 plus x close parentheses to the power of n comma space w e space h a v e comma 1 plus n h plus fraction numerator n open parentheses n minus 1 close parentheses h squared over denominator 2 end fraction plus... equals open parentheses 1 plus h close parentheses to the power of n rightwards double arrow n h plus fraction numerator n open parentheses n minus 1 close parentheses h squared over denominator 2 end fraction plus... equals open parentheses 1 plus h close parentheses to the power of n minus 1

Answered by Vimala Ramamurthy | 4th Oct, 2015, 12:38: PM