Question

Could you help me with finding the sum of 7+77+777+...+777...77? Where in the 777...77 are n sevens.

Answer 1

http://answers.yahoo.com/question/index?qid=20110609190829AA0SDYC

Answer 2

The link that @anusha.p pasted above seems to have the solution to this.

Answer 3

7[10^(n + 1) - 9n - 10]/81.
substitute n=7

Answer 4

Thanks everyone:)

Answer 5

the question itself cannot be used to find sum , instead we need to make it to form whose sum which we can calculate .I call this process beautification,
so here by "beautifying" the expression:

\[\large 7+77+777+777+7777+.......\]
\[\large =\frac{7}{9}\times(9+99+999+9999+.....n terms)\]
\[\large =\frac{7}{9}\times((10^1-1+10^2-1+10^3-1+......2n \;terms)\]
\[\large =\frac{7}{9}\times((10^1+10^2+10^3+.....+10^n)-(1+1+1+1+...+n\;terrms))\]
\[\large =\frac{7}{9}\times\frac{10(10^n-1)}{10-1})-(n)\]

make further simplification if u need :)
srry i am slow at typing

Answer 6

@viodhora?

Answer 7

thanks a lot:)