" 5.सिद्ध कीजिए कि- "n!(n+2)=n!+(n+1)!

सिद्ध कीजिए कि 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

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

lim_ (n rarr oo) n ^ (- n ^ (2)) ((n + 1) (n + (1) / (2)) (n + (1) / (2 ^ (2))) .... (n + (1) / (2 ^ (n-1)))) ^ (n)

Find the value of n if: 2n! n! =(n+1)(n-1)(!(2n-1)!

Sum of the series S_(n) =(n) (n) + (n-1) (n+1) + (n-2) (n+2) + …+ 1(2n-1) is

The coefficient of 1/x in the expansion of (1+x)^(n)(1+1/x)^(n) is (n!)/((n-1)!(n+1)!) b.((2n)!)/((n-1)!(n+1)!) c.((2n-1)!(2n+1)!)/((2n-1)!(2n+1)!) d.none of these

If alpha in R, n in N " and " n + 2 (n - 1)+ 3 (n-2) + …… +(n-1)2 + n.1 = alpha n ( n + 1) (n + 2) , " then " alpha =