`.^(n) C_(2) + .^(7)C_(3) = .^(8) C_(3)`

Prove that .^(7)C_(2)+^(7)C_(3)=^(8)C_(3)

Find .^(n)C_(3) , if .^(n)C_(7)=.^(n)C_(4) .

If .^(n)C_(8)=.^(n)C_(6) , find .^(n)C_(3) .

Prove that .^(n-1)C_(3)+.^(n-1)C_(4) gt .^(n)C_(3) if n gt 7 .

If .^(n)C_(8) = .^(n)C_(2) , find .^(n)C_(2) .

The sum 3 .^(n)C_(0)-8.^(n)C_(1)+13 .^(n)C_(2)-18xx.^(n)C_(3)+.... is less than

The sum of the following series upto'n' terms is given by S=^(n)C_(0)+2.^(n)C_(1)+4^(n)C_(2)+7.^(n)C_(3)+11.^(n)C_(4)+