Show tha, 1+1/(2!)+1/(4!)+....=1/2(e+1/e) | CLASS 12 | SERIES | MATHS | Doubtnut

Show that, e^x+e^(-x)=2(1+x^2/(2!)+x^4/(4!)+....)

Prove that, 1/(1.2)-1/(2.3)+1/(3.4)-.....=2log_e2-1

Show that, log_e2=1/(1.2)+1/(3.4)+1/(5.6)+.....infty

Show tha , lim_(ntooo) ((1)/( n +1)+(1)/( n +2)+ . . . +(1)/( 6 n))= log 6 .

The sum of the series 1/(2!)-1/(3!)+1/(4!)-... upto infinity is (1) e^(-2) (2) e^(-1) (3) e^(-1//2) (4) e^(1//2)

If e_(1) be the eccentricity of a hyperbola and e_(2) be the eccentricity of its conjugate, then show that the point (1/e_(1) , 1/e_(2)) lies on the circle x^(2) + y^(2) = 1 .

int (e ^ (2x)) / ((e ^ (x) -1) ^ ((1) / (4))) dx

Sum of the infinite series (1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+...to oo(e)/(3) b.e c.(e)/(2)d . none of these