25. Sum the series 7 .77+777 +... to n terms.

1.	25. Sum the series 7 .77+777 +... to n terms.
Answer» TO FIND: 7+77+777+7777+………n If the series has: 2 terms, the sum = 7(12) 3 terms, the sum = 7(123) 4 terms, the sum = 7 (1234) 5 terms, the sum = 7 (12345) ……………………. 9 terms, the sum = 7 (123456789)……Formula But for finding the sum , if series has more than 9 terms, we may use a different formula… = 7 + 77 + 777 + 7777 + ……… n = 7( 1 + 11 +111 + 1111 + ………. n/7 ) = 7(1 +11+111+1111+……..n/7) ( 9/9) = (7/9) ( 9 + 99 + 999 + 9999……9n/7 ) =(7/9){(10–1)+(100–1)+(1000–1)+(10000–1)+…….. +(10^n -1) } =(7/9)( (10+1010+1010²+1010^3+………..1010^(n-1) - (1* n) } =7/9 *[{ 10 (10^n —1)/9}— n ] …..Formula( using the sum to n terms of a G.P. series like my answer if you find it useful!

Answer»

TO FIND: 7+77+777+7777+………n

If the series has:

2 terms, the sum = 7*(12)

3 terms, the sum = 7*(123)

4 terms, the sum = 7 *(1234)

5 terms, the sum = 7 *(12345)

…………………….

9 terms, the sum = 7 *(123456789)……Formula

But for finding the sum , if series has more than 9 terms, we may use a different formula…

= 7 + 77 + 777 + 7777 + ……… n

= 7( 1 + 11 +111 + 1111 + ………. n/7 )

= 7(1 +11+111+1111+……..n/7) * ( 9/9)

= (7/9) ( 9 + 99 + 999 + 9999……9n/7 )

=(7/9){(10–1)+(100–1)+(1000–1)+(10000–1)+…….. +(10^n -1) }

=(7/9)( (10+10*10+10*10²+10*10^3+………..10*10^(n-1) - (1* n) }

=7/9 *[{ 10 (10^n —1)/9}— n ] …..Formula( using the sum to n terms of a G.P. series

like my answer if you find it useful!

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