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# 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, 3 months ago

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

Could u explain how u got this?? · 2 years, 10 months ago

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

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