Find the value of (1.01)10 + (1 − 0.01)¹⁰ correct to 7 places of decimal.

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Solution

$(1.01)^{10} + (1 - 0.01)^{10} = (1 + 0.01)^{10} + (1 - 0.01)^{10} = 2 [{}^{10}C_{0} \times (0.01)^{0} + {}^{10}C_{2} \times (0.01)^{2} + {}^{10}C_{4} \times (0.01)^{4} + {}^{10}C_{6} \times (0.01)^{6} + {}^{10}C_{8} \times (0.01)^{8} + {}^{10}C_{10} \times (0.01)^{10}] = 2 (1 + 45 \times 0.0001 + 210 \times 0.00000001 + . . .) = 2 (1 + 0.0045 + 0.00000210 + . . .) = 2.0090042 + . . .$

Hence, the value of (1.01)10 + (1 − 0.01)¹⁰ correct to 7 places of the decimal is 2.0090042

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