সিরিজের যোগফল (1^2)/(2!)+(2^2)/(3!)+(3^2)/(4!)+is\r\n\r\ne+1\ r\nb. e-1\r\nc. 2e+1\r\nd...

Value of 1/(r_(1)^2)+ 1/(r_(2)^2)+ 1/(r_(3)^2)+ 1/(r_()^2) is :

Find sum_(r=1)^(n)(1^(2)+2^(2)+3^(3)+...+r^(2))/(r+1)

Define the collection {E_1,E_2,E_3,"....."} of ellipses and {R_1,R_2,R_3,"....."} of rectangles as follows: E_1= (x^2)/(9)+(y^2)/(4)=1 , R_1 : rectangle of largest area, with sides parallel to the axes, inscribed in E_1 , E_n : ellipse (x^2)/(a_(n)^(2))+(y^2)/(b_(n)^(2))=1 of largest are inscribed in R_(n-1), n gt 1 . then which of the following options is/are corrct?

Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)

The value of 1/(r_(1)^(2))+1/(r_(2)^(2))+1/(r_(2)^(3))+1/(r^(2)) , is

If t=(1^(2)+2^(2)+3^(2)+...r^(2))/(1^(3)+2^(3)+3^(3)+....+r^(3)), S_(n) = overset(n) underset(r=1) sum(-1)^(r)t_(r) then lim_(n to oo) ((1)/(3)-S_(n))=

If sum_(r=1)^(n)r(r+1)(2r+3)=an^(4)+bn^(3)+cn^(2)+dn+e , then.