The value of the expression `log_(2)(1+(1)/(2) sum_(k=1)^(11) ""^(12)C_(k))`:

The value of the expression (sum_(r=0)^(10)C_(r))(sum_(k=0)^(10)(-1)^(k)(^^10C_(k))/(2^(k))) is :

The value of the expression (sum_(r=0)^10 "^10 C_r)(sum_(k=0)^10 (-1)^k (^10 C_k)/2^k) is :

Evaluate sum_(k=1)^(11)(2+3^(k))

Evaluate sum_(k=1)^(11)(2+3^(k))

For any integer K , let alpha_(k)=cos((kpi)/(7))+isin((kpi)/(7))," where " i=sqrt(-1) The value of the expression (sum_(k=1)^(12)|alpha_(k+1)-alpha_(k)|)/(sum_(k=1)^(3)|alpha_(4k-1)-alpha_(4k-2)|)

Evaluate sum_(k=1)^(11)(2+3^k)

Evaluate sum_(k=1)^11(2+3^k)

Evaluate sum_(k=1)^11(2+3^k)

Evaluate sum_(k=1)^11(2+3^k)

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