" 18."1+2+3+...+n<(1)/(8)(2n+1)^(2)

.If 20 , 19 1/ 3 , 18 2/ 3 ,,... ,are in A.P.,and sum to 'n' terms of the series is 300 then '2n' is ] , [ 1) 25 2) 50 3) 75 4) 18

Fill in the blanks in the following table , given that a is the first term, d the common difference and a_(n) the nth term of the A.P: (i) a=7, d=3, n=8, a_(n)=? (ii) a= - 18, n=10, a_(n)=0, d=? 0= -18+(10-1) d rArr 10d-d=18 9d=18 rArr d=(18)/(9)=2 d=2 (iii) a=? , d= -3, n=18, a_(n)= - 5 (iv) a= -18.9, d=2.5, n=?, a_(n)=3.6

Show that 3C_0-8C_1 + 13C_2 - 18C_3 + ..... + (n+1)^(th) term = 0

The sum to (n + 1) terms of the series 3.nC_0 - 8.nC_1 +13.nC_2 -18.nC_2 +........ is

Electronic transition in He ion takes from n_2 to n_1 shell such that : 2n_2 + 3n_1 = 18 , 2n_2 - 3n_1 = 6 What will be the total number of photons emitted when electrons transit to n_1 shell ?

S (n) = sum_ (r = 1) ^ (n) ((cos (2 * 3 ^ (r-1) alpha)) / (sin (3 ^ (r) alpha), alpha = 18 ^ (@) ) and P (n) = sum_ (r = 1) ^ (n) (cos (3 * 2 ^ (r-1) beta)) / (cos (2 ^ (r) beta)), beta = 36 ^ ( @)

If 1*1!+2*2!+3*3!+ . . .+n*n ! =(n+1)!-1 then show that, 1*1!+2*2!+3*3!+ . . . +n*n! +(n+1)(n+1)! =(n+2)!-1

Suppose n is a natural number such that |i + 2i^2 + 3i^3 +...... + ni^n|=18sqrt2 where i is the square root of -1 . Then n is