find the sum of 7+77+777+....n terms
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Answered by
9
Hi Buddy !
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Let the sum = S
S = 7+77+777+...+n
S= 7(1+11+111+...+n)
Multiply and divide by 9
we get,
S = 7/9 (9+99+999+...+n)
S = 7/9 [10-1+100-1+1000-1+...+n]
S = 7/9 [ 10-1+ 10²-1 + 10³-1+...n]
Take all multiples of 10 which will form a GP all these -1's separate
S = 7/9 [10+10²+10³..-n]
S = 7/9 [10 (10^n-1)/9-n]
S = 70/81(10^n-1)-n]
____________________________________________________________
_____________________________________________________________
Let the sum = S
S = 7+77+777+...+n
S= 7(1+11+111+...+n)
Multiply and divide by 9
we get,
S = 7/9 (9+99+999+...+n)
S = 7/9 [10-1+100-1+1000-1+...+n]
S = 7/9 [ 10-1+ 10²-1 + 10³-1+...n]
Take all multiples of 10 which will form a GP all these -1's separate
S = 7/9 [10+10²+10³..-n]
S = 7/9 [10 (10^n-1)/9-n]
S = 70/81(10^n-1)-n]
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mysticd:
7th and 8th lines need corrections, plz check
done :)
in 7th line change third term 1000-1
and it is not n change it as n terms
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11
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