^mC_r+ ^mC_r-1ⁿC₁+^mC_r-2. ⁿC₂+………..+ ⁿC_r =

Sum of the last 20 coefficients in the expansion of (1+x)³⁹, when expanded in ascending powers of x, is

The 4^th term of ⁶(x+2/x²)⁶ is

If x is so small that x² and higher powers of x may be neglected then (1-x)^1/2(1+x)^2/3/(1-x)^1/2

3√1003 -3√997

If n is even then C₀²-C₁²+C₂²-……….+(-1)ⁿ C_n² =

The number of non-zero terms in the expansion of (1+3√2x)⁹+(1+3√2x)⁹is equal to:

If the coefficient of rth term and (r + l)th term in the expansion of (1 + x)²⁰ are in the ratio 1 : 2, then r is equal to:

C₀+C₁/2+C₂/2²+C₃/2³+.....C_n/2ⁿ

C₀-2. C₁+3. C₂………..+(-1)ⁿ(n+1).C_n =