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mathmath333
 one year ago
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mathmath333
 one year ago
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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} & \normalsize \text{Find the number of terms in }\hspace{.33em}\\~\\ & (a+b+c+d)^{50} \hspace{.33em}\\~\\ \end{align}}\)

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.2have u tried using binomial :)

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.2u can see this if u want http://mathforum.org/library/drmath/view/68607.html :)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\LARGE { 53\choose 3}\)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I got mine answer a bit longer way... \[(a+b+c+d)^{50} \\ =(a+b)^{50}+c_1(a+b)^{49}(c+d)+c_2(a+b)^{48}(c+d)^2+ \cdots \\ +c_{24}(a+b)^{26}(c+d)^{24}+c_{25}(a+b)^{25}(c+d)^{25}+c_{26}(a+b)^{24}(c+d)^{26} + \cdots \\+ c_{48}(a+b)^{2}(c+d)^{48}+c_{49}(a+b)(c+d)^{49}+(c+d)^{50} \\ \\ \text{ so we have terms of that thingy } = \\ 51+50(2)+49(3)+\cdots+27(25)+26(26)+25(27)+\cdots +3(49)+2(50)+51\] \[=2 \cdot \sum_{i=1}^{25}i(52i)+26 \cdot 26 \\ =2 \sum_{i=1}^{25}(52ii^2)+26 \cdot 26 \\ =2 ( 52 \cdot \frac{25(25+1)}{2} \frac{25(25+1)(2 \cdot 25+1)}{2})+26 \cdot 26 \\ \\ \]\[=52(25)(25+1)\frac{25(25+1)(2 \cdot 25+1)}{3}+26^2 \\ =23426\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2lol i did say a bit longer

freckles
 one year ago
Best ResponseYou've already chosen the best response.2here is an example if what I did using a smaller exponent \[(a+b+c+d)^{3} \\ =([a+b]+[c+d])^3 \\ =(a+b)^3+c_1(a+b)^2(c+d)+c_2(a+b)(c+d)^2+(c+d)^3 \\ \text{ number of terms } =4+3(2)+2(3)+4\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2(a+b)^3 <expanding this will give you 3+1 (a+b)^2(c+d) <expanding this will give you well (3 terms)(c+d) which is 3+3 or 3(2) terms and so on...
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