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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, 5 months ago

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Use binomial expansion for (\(1+3)^{50}\) and answer would be \(4^{50}-3^{50}\) Gopinath No · 3 years, 5 months ago

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@Gopinath No Could u explain how u got this?? Tanya Gupta · 3 years ago

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@Gopinath No the expansion is \((3+1)^{50}\) Snehdeep Arora · 3 years, 5 months ago

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i think \( \dbinom{50}{0}\)\(3^{50}\)(the first term of the expansion of \((3+1)^{50}\)) is missing Snehdeep Arora · 3 years, 5 months ago

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