If 3 ^5 C ₀+8 ^5 C ₁+13 ^5 C ₂+18 ^5 C ₃+23 ^5 C ₄+28 ^5 C ₅= k 2^4 , then k =

Step-by-step solution

aligned 3 ^5 C₀+8 ^5 C₁ & +13 ^5 C₂+18 ^5 C₃ & +23 ^5 C₄+ .+28 ^5 C₅=k 2^4 aligned aligned =3 ^5 C₀+(5+3)^5 C₁+ & (10+3)^5 C₂+(15+3)^5 C₃ & +(20+3)^5 C₄+ .+(25+3)^5 C₅ aligned aligned =3 ( ^5 C₆+ ^5 C₁ . & .+ ^5 C₂+ ^5 C₃+ ^5 C₄+ ^5 C₅ ) & +5 ( ^5 C₁+2 ^5 C₂+3 ^5 C₃+4 ^5 C₄+5^5 C₅ ) aligned =3 2^5+5 (5+2 5 4 2 +3 5 4 2 +4 5+5 ) aligned & =3 2^5+5 80 & =3 2 2^4+25 2^4 & =(6+25) 2^4=31 2^4 aligned array r 3 ^5 C₀+8 ^5 C₁+13 ^5 C₂+18 ^5 C₃ +23 ^5 C₄+28 ^5 C₅=31 2^4 array aligned & k 2^4=31 2^4 & k=31 aligned