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प्रश्न
Using binomial theorem, find the value of (102)4
उत्तर
(102)4 = (100 + 2)4
= 4C0 (100)4 (2)0 + 4C1 (100)3 (2)1 + 4C2 (100)2 (2)2 + 4C3 (100)1 (2)3 + 4C4 (100)0 (2)4
Since, 4C0 = 4C4 = 1, 4C1 = 4C3 = 4, 4C2 = 6
∴ (102)4 = 1(100000000)(1) + 4(1000000)(2) + 6(10000)(4) + 4(100)(8) + 1(1)(16)
= 100000000 + 8000000 + 240000 + 3200 + 16
= 108243216
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