×

# Summing Combinatories

Is there any way to sum up the following series ::

{50 C 1} {3^49} + {50 C 2} {3^48} + {50 C 3} {3^47} + ................................... ...................................... {50 C 48} {3^2} + {50 C 49} {3^1} + {50 C 50} {3^0}

Note by Santanu Banerjee
3 years ago

Sort by:

Use binomial expansion for ($$1+3)^{50}$$ and answer would be $$4^{50}-3^{50}$$ · 3 years ago

Could u explain how u got this?? · 2 years, 7 months ago

the expansion is $$(3+1)^{50}$$ · 3 years ago

i think $$\dbinom{50}{0}$$$$3^{50}$$(the first term of the expansion of $$(3+1)^{50}$$) is missing · 3 years ago