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InterviewSolution
| 1. |
Using binomial theorem,indicate which number is larger (1.1)^10000 or 1000 |
| Answer» (1.1)^(10000) = (1 + 0.1)^(10000)use formula,(x + y)^n = nC0.x^n + nC1.x^(n-1)y + nC2.x^(n-2)y^2 + ........+nCn.y^n(1 + 0.1)^(10000) = 10000C0.(1)^(10000) + 10000C1.(1)^9999(0.1) + ....... other terms= 1 × 1 + 10000 × 0.1 + ......... other terms .= (1 + 1000 + .......other terms ) > 1000hence, (1.1)^(10000) > 1000<br>(1.1)^(10000) = (1 + 0.1)^(10000)use formula,(x + y)^n = nC0.x^n + nC1.x^(n-1)y + nC2.x^(n-2)y^2 + ........+nCn.y^n(1 + 0.1)^(10000) = 10000C0.(1)^(10000) + 10000C1.(1)^9999(0.1) + ....... other terms= 1 × 1 + 10000 × 0.1 + ......... other terms .= (1 + 1000 + .......other terms ) > 1000hence, (1.1)^(10000) > 1000 | |