Find the `underset(k=1)overset(oo)sumunderset(n=1)overset(oo)sumk/(2^(n+k))`.

If x = underset(n-0)overset(oo)sum a^(n), y= underset(n =0)overset(oo)sum b^(n), z = underset(n =0)overset(oo)sum C^(n) where a,b,c are in A.P. and |a| lt 1, |b| lt 1, |c| lt 1 , then x,y,z are in

Prove that underset(rles)(underset(r=0)overset(s)(sum)underset(s=1)overset(n)(sum))""^(n)C_(s) ""^(s)C_(r)=3^(n)-1 .

The value of cot (underset(n=1)overset(23)sum cot^(-1) (1 + underset(k=1)overset(n)sum 2k)) is

If n and l are respectively the principal and azimuthal quantum numbers , then the expression for calculating the total number of electrons in any energy level is : (a) underset(l=0)overset(l=n)sum2(2l+1) (b) underset(l=1)overset(l=n)sum2(2l+1) (c) underset(l=0)overset(l=n)sum2(2l+1) (d) underset(l=0)overset(l=n-1)sum2(2l+1)

Find the value underset(n rarr oo)("lim") underset(k =2)overset(n)sum cos^(-1) ((1 + sqrt((k -1) k(k + 1) (k + 2)))/(k(k + 1)))

Calculate the energy in fusion reaction . overset(2)underset(1).H +overset(2)underset(1).H to overset(4)underset(2).He + n " where BE of " overset(2)underset(1).H=2.23 MeV " and of " overset(4)underset(2).He =7.73 MeV

underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-n^(2)) is equal to

Find the value of underset(r = 0) overset(oo)sum tan^(-1) ((1)/(1 + r + r^(2)))

Which of the following structures for N_(2)O gives a more accurate representation of the molecule ? :N-=underset((T))(overset(+)(N))-overset(* *^(-))underset(* *)O: overset(* )underset(* *)N= overset(o+)underset((II))(N)=underset(* *) overset(* *)O

Let S_(k)=underset(ntooo)limunderset(i=0)overset(n)sum(1)/((k+1)^(i))." Then "underset(k=1)overset(n)sumkS_(k) equals