The total number of different terms in the product `(.^(101)C_(0) - .^(101)C_(1)x+.^(101)C_(2)x^(2)-"….."-.^(101)C_(101)x^(101))(1+x+x^(2)+"…."+x^(100))^(101)` is `"____"`.

The number of terms in the expansion (1+x)^(101)(1-x+x^(2))^(100) is

The coefficient of x^(50) in (x+^(101)C_(0))(x+^(101)C_(1)).....(x+^(101)C_(50)) is

The coefficient of x^(50) in (x+^(101)C_(0))(x+^(101)C_(1)).....(x+^(101)C_(50)) is

The coefficient of x^(50) in (x+^(101)C_(0))(x+^(101)C_(1)).....(x+^(101)C_(50)) is

The sum of the series (.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101))/(.^(101)C_(100)) is "____" .

The sum of the series (.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101))/(.^(101)C_(100)) is "____" .

The number of nonzero terms in the expansion of (x+2 sqrt2)^(101)-(x-2 sqrt2)^(101) is