krishnakanjirakattil

Use the following steps to show that the sequence tn = 1 + 1/2 + 1/3 + . . .+ 1/n - In n has a limit. (The value of the limit is denoted by gamma and is called Euler's constant.) Draw a picture like Figure 6 on page 703 with f(x) = 1/x and interpret tn as an area to show that tn > 0 for all n. Interpret tn - tn+1 = [In(n+1) - In n] - 1/n + 1 As a difference of areas to show that tn - tn+1 > 0. Therefore, {tn} is a decreasing sequence. Use the Monotonic Sequence Theorem to show that {tn} is convergent. Use your graphics calculator to calculate t999. Copy all digits. t999= Go to Wikipedia and find the value of gamma with 30 digits. Copy them. gamma=