The sum `sum_(k=1)^20 k (1)/(2^(k))` is equal to

sum_(x-1)^(20)k(1)/(2^(k)) is equal to

The sum sum_(k=1)^(n)k(k^(2)+k+1) is equal to

sum_(k=1)^(3n)6nC_(2k-1)(-3)^(k) is equal to

sum_(k=0)^(20)(.^(20)C_(k))^(2) is equal to

The sum sum_(k=1)^(100)(k)/(k^(4)+k^(2)+1) is equal to

Let S_(k) , be the sum of an infinite geometric series whose first term is kand common ratio is (k)/(k+1)(kgt0) . Then the value of sum_(k=1)^(oo)(-1)^(k)/(S_(k)) is equal to