# What is the sum of #7+77+777+7777+...# to #n# terms ?

##### 1 Answer

Nov 7, 2016

#### Explanation:

Note that

Hence we can write a formula for the

#a_k = 7/9(10^k - 1)" "# for#k = 1,2,3...#

Let:

#b_k = 7/9(10^k) = 70/9*10^(k-1)#

This is in the form

The sum to

#S_n = (b(r^n-1))/(r-1) = 70/9*(10^n-1)/(10-1) = 70/81*(10^n-1)#

Hence:

#sum_(k=1)^n a_k = 70/81(10^n-1) - 7/9n#