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..Question..
Find the sum upto nth term in the given series
☯︎ 4 + 44 + 444 + - - - - - - to nth term
☯︎ 8 + 88 + 888 + - - - - - - to nth term
..Answer..
1 ) The given term is ➪
= 4 + 44 + 444 + - - - - - - - to nth term
= ( 4 + 44 + 444 + - - - - - - - to nth term )
= 4 ( 1 + 11 + 111 + - - - - - - to nth term )
= 4/9 ( 9 + 99 + 999 + - - - - - - to nth term )
= 4/9 { (10-1) + (100-1) + (1000-1) + - - - to nth term }
= 4/9 { ( 10 + 100 + 1000 + - - - to nth term ) - ( 1 + 1 + 1 + - - - to nth term ) }
= 4/9 [ { 10 × { ( 10 )^n - 1 } / ( 10 - 1 ) - n ]
= 4/9 { 10 ( 10^n - 1 ) / 9 - n }
2 ) The given term is ➪
= 8 + 88 + 888 + - - - - - - - to nth term
= ( 8 + 88 + 888 + - - - - - - - to nth term )
= 8 ( 1 + 11 + 111 + - - - - - - to nth term )
= 8/9 ( 9 + 99 + 999 + - - - - - - to nth term )
= 8/9 { (10-1) + (100-1) + (1000-1) + - - - to nth h term }
= 8/9 { ( 10 + 100 + 1000 + - - - to nth term ) - ( 1 + 1 + 1 + - - - to nth term ) }
= 8/9 [ { 10 × { ( 10 )^n - 1 } / ( 10 - 1 ) - n ]
= 8/9 { 10 ( 10^n - 1 ) / 9 - n }
_____________________
Give a look here ,
- To calculate AP , use :-
- a + ( n - 1 ) d
- and
- b - a = c - b
ㅤㅤㅤ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂
ㅤ
Answered by
9
..Question..
Find the sum upto nth term in the given series
☯︎ 4 + 44 + 444 + - - - - - - to nth term
☯︎ 8 + 88 + 888 + - - - - - - to nth term
..Answer..
1 ) The given term is ➪
= 4 + 44 + 444 + - - - - - - - to nth term
= ( 4 + 44 + 444 + - - - - - - - to nth term )
= 4 ( 1 + 11 + 111 + - - - - - - to nth term )
= 4/9 ( 9 + 99 + 999 + - - - - - - to nth term )
= 4/9 { (10-1) + (100-1) + (1000-1) + - - - to nth term }
= 4/9 { ( 10 + 100 + 1000 + - - - to nth term ) - ( 1 + 1 + 1 + - - - to nth term ) }
= 4/9 [ { 10 × { ( 10 )^n - 1 } / ( 10 - 1 ) - n ]
= 4/9 { 10 ( 10^n - 1 ) / 9 - n }
2 ) The given term is ➪
= 8 + 88 + 888 + - - - - - - - to nth term
= ( 8 + 88 + 888 + - - - - - - - to nth term )
= 8 ( 1 + 11 + 111 + - - - - - - to nth term )
= 8/9 ( 9 + 99 + 999 + - - - - - - to nth term )
= 8/9 { (10-1) + (100-1) + (1000-1) + - - - to nth h term }
= 8/9 { ( 10 + 100 + 1000 + - - - to nth term ) - ( 1 + 1 + 1 + - - - to nth term ) }
= 8/9 [ { 10 × { ( 10 )^n - 1 } / ( 10 - 1 ) - n ]
= 8/9 { 10 ( 10^n - 1 ) / 9 - n }
_____________________
Give a look here ,
- To calculate AP , use :-
- a + ( n - 1 ) d
- and
- b - a = c - b
ㅤㅤㅤ꧁ I AM SHREYA ꧂
ㅤ
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