Question

find the sum to n terms of 7+77+777+............​

Answer 1

Step-by-step explanation:

inshallah it helps uuh..❤

Answer 2

Question :-

• find the sum to n terms of 7+77+777+...+n

Solution :-

$7+77+777 +... + n</p><p>$

Take 7 common

$= 7 [1+11+111 + ... + n]$

Now multiply and devide by 9

$= \: \frac{7}{9} (9 + 99 + 999 + ... + n)$

Now apply series transformation rule

$= \frac{7}{9} \: \: [ \: \: (10 - 1) + (100 - 1) + (100 0 - 1) + ... + (n \: \: terms) - (1 + 1 + 1 + ... + n \: \: terms) ] \\ \\ = \frac{7}{9} [ (10) + (100) + (1000) +( 9999) + ... + n \: ] = \frac{7}{9} [ \frac{10(10 {}^{n} - 1 )}{10 - n} - n] \\ \\ = \frac{7}{81} [10(10 {}^{n} - 1) - n] \: \: \: answer$