The sum of the series 34·8-3·54·8·12+3·5·74·8·12·16-.......... is
32-34
23-34
32-14
23-14
Explanation for the correct option
Given: 34·8-3·54·8·12+3·5·74·8·12·16-..........
Let, S=34·8-3·54·8·12+3·5·74·8·12·16-..........
add 1-14to both sides
⇒S+1-14=1-14+34·8-3·54·8·12+3·5·74·8·12·16-..........⇒S+34=1-11·14+1438-1438512+1438512716-........⇒S+34=1-11·14+1·31·2142-1·3·51·2·3143+................
Let p=1,q=2,x=12
S+34=1-p1xq+p·p+q1·2xq2-p·p+q(p+2q)1·2·3xq3+............
expansion of (1+x)-pq=1-p1xq+p·p+q1·2xq2-p·p+q(p+2q)1·2·3xq3+............
S+34=(1+x)-pq
Put p=1,q=2,x=12
⇒S+34=(1+12)-12⇒S+34=32-1⇒S+34=23⇒S=23-34
Hence, OptionB is correct.
Verify the following :
(i) 37×(56+1213)=(37×56)+(37×1213) (ii) −154×(37+−125)=(−154×37)+(−154×−125) (iii) (−83+−1312)×56=(−83×56)+(−1312×56) (iv) −167×(−89+−76)=(−167×−89)+(−167×−76)
Re-arrange suitably and find the sum in each of the following :
(i)1112+−173+112+−252
(ii)−67+−56+−49+−157
(iii)35+73+95+−1315+−73
(iv) 413+−58+−813+913
(v)23+−45+13+25
(vi) 18+512+27+712+97+−516
Fill in the blanks.
(i) (−317)+(−125)=(−125)+(.....)
(ii) −9+−218=(......)+(−9)
(iii) (−813+37)+(−134)=(......)+[37+(−134)]
(iv) −12+(712+−911)=(−12+712)+(.....)
(v) 19−5+(−311+−78)={19−5+(.....)}+−78
(vi) −167+.....=......+−167=−167
Fill in the blanks:
(i) −4×79=79× ___
(ii) 511×−38=−38× ___
(iii) 12×(34+−512)=12× ____ +(×)−512
(iv) −45×57×___ =(−45×57)×−89