Evaluate `(n!)/((n-r)!)` when n= 6 and r=2 ?

Evaluate (n!)/((n-r)!) , when n = 9, r = 5

Evaluate (n!)/(r!(n-r)!) , when n = 5, r = 2.

Evaluate sum_(r=1)^(n)rxxr!

If a_n =(2n-3)/6 , then find a_(10) ?

(i) Write sum_(r=1)^(n)(r^(2)+2) in expanded form. (ii) Write the series (1)/(3)+(2)/(4)+(3)/(5)+(4)/(6)+"…"+(n)/(n+2) in sigma form.

If sum_(r=1)^n t_r=n/8(n+1)(n+2)(n+3), then find sum_(r=1)^n1/(t_r)dot

If sum_(r=1)^(n)T_(r)=(n(n+1)(n+2)(n+3))/(12) where T_(r) denotes the rth term of the series. Find lim_(nto oo) sum_(r=1)^(n)(1)/(T_(r)) .

If (r)_n , denotes the number rrr... (n digits) , where r = 1,2,3,...,9 and a=(6)_n,b=(8)_n,c=(4)_(2n) , then

if .^(2n)C_(2):^(n)C_(2)=9:2 and .^(n)C_(r)=10 , then r is equal to