Solve - 31 - 10C1 - 32 - 10C2 - 33 - 10C3 - - - 310- 10C10 - -

3^1× ^10C_1+3^2× ^10C_2+3^3× ^10C_3+....3^10× ^10C_10=? (1+x)^n=^nC_0+^nC_1 × ax^1+ ^nc_2x^2+......^nC_nx^n Put x=3 and n=10 (1+3)^10= ...

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Combination

Solve : 31 ...

Question

Solve : $3^{1} \times^{10} C_{1} + 3^{2} \times^{10} C_{2} + 3^{3} \times^{10} C_{3} + . . . . + 3^{10} \times^{10} C_{10} =$ ?

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Solution

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Similar questions

(21 C_{1} - 10 C_{1}) + (^{21} C_{2} - 10 C_{2}) + (21 C_{3} - 10 C_{3}) + (21 C_{4} - 10 C_{4}) + \dots . + (21 C_{10} - 10 c_{10})

(^{21} C_{1} -^{10} C_{1}) + (^{21} C_{2} -^{10} C_{2}) + (^{21} C_{3} -^{10} C_{3}) + (^{21} C_{4} -^{10} C_{4}) + \dots + (^{21} C_{10} -^{10} C_{10})

\frac{1}{2}

^{10} C_{0} -

^{10} C_{1} +

2 \cdot^{10} C_{2} -

2^{2} \cdot^{10} C_{3}

2^{9} \cdot^{10} C_{10}

(^{21} C_{1} -^{10} C_{1}) + (^{21} C_{2} -^{10} C_{2}) + (^{21} C_{3} -^{10} C_{3}) + (^{21} C_{4} -^{10} C_{4}) + . . . + (^{21} C_{10} -^{10} C_{10})

^{10} C_{1} +^{10} C_{2} +^{10} C_{3} + . . . +^{10} C_{9}

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