Find the value of (1.01)10 + (1 − 0.01)

$(1.01)^{10}+(1-0.01)^{10}$

$=(1+0.01)^{10}+(1-0.01)^{10}$

$=2\left[{ }^{10} C_{0} \times(0.01)^{0}+{ }^{10} C_{2} \times(0.01)^{2}+{ }^{10} C_{4} \times(0.01)^{4}+{ }^{10} C_{6} \times(0.01)^{6}+{ }^{10} C_{8} \times(0.01)^{8}+{ }^{10} C_{10} \times(0.01)^{10}\right]$

$=2(1+45 \times 0.0001+210 \times 0.00000001+\ldots)$

$=2(1+0.0045+0.00000210+\ldots)$

$=2.0090042+\ldots$

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