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Methods of Induction and Binomial Theorem — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsMethods of Induction and Binomial Theorem1 Mark
Question
Show that $C_1+C_2+C_3+\ldots . .+C_7=127$
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Answer

Since $C_0+C_1+C_2+C_3+\ldots . .+C_n=2^n$
Putting $n = 7,$ we get
$C_0+C_1+C_2+\ldots . .+C_7=2^7$
$\therefore C_0+C_1+C_2+\ldots . .+C_7=128$ But, C0 = 1
$\therefore 1+C_1+C_2+\ldots . .+C_7=128$
$\therefore C_1+C_2+\ldots . .+C_7=128-1=127$

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