Question

10. Write the fir rite the first four terms of (1 + )", if mis a positive integer 11. Find the general term for 1 - 2 + 3 - 4 + .. 12. Find 2 (k+ 2 ) for k = 1 to k = 4. 13. Find TT (K + 1) for k = 1 to k = 4.

Answer 1

S01910) We write first four terms of (1+1.)" as follow By Brnonuch theorem we know that 1. (a+b)" - Înc. ankok (1+ļ)". MCM + mc, m-4 (1) + m«,.-2 ()* + MG im-> (+)? + MC., m4. (4.)"+...... (144)" 2 16.+ me, () + mę (+)2 + m (1) + may (1) 4+.... First four terms are mo, mg, () ., m (!), MA () Somly To finel general term for 1-2 +3-4+--- "*' - 1-2 +3-4+. . Dol → E (-1)"?'N = 1-2+3 -4+-.. is inequine gerveral form Soin 127 To find {(k+2) for k=1 to k=4 Неме Ź (k+2) = (1+2)+(2+2)+ (3+2) + (4+2) = 3 +4+5+6 = 18 ka

3) To fing TT (k+1) -for k=1 to k= 4 (k+1) = (1+1). (2+1). (3+1)-(4+1) - 2 -3 -4.5 6-20 = (k+t) = 120 = 120 ku Soin 14 5 , 5-4.3.21 E = 5.4.3 = 60 2 24 51 - 60 21 Solis) 6 choose 3 = 6 Choose 3 = 6C = 6! 6! = 4:5.4.11.20 65.43 3-2 RL - 20 31.31 1. 6 Choose 3 = 20 Abore is our solution