a)2¹⁺²⁺³⁺⁴⁺ ⁺¹⁶=(2²)ⁿ⁺⁷⇒2¹³⁶=2²⁽ⁿ⁺⁷⁾ 136=2(n+7)⇒68=n+7⇒n=61
apl. suma gauss 1+2+3+...+16=16*17/2=136
b)(2²)²⁺⁴⁺⁶⁺ ⁺²⁰=(2²)ⁿ⁽ⁿ⁺¹⁾⇒2²²⁰=2²ⁿ⁽ⁿ⁺¹⁾⇒220=2n(n+1)⇒110=n(n+1)
(110=n²+n m am incuiat,poate ai tu vreo idee)
apl. SG 2(1+2+3+...+10)=2x10x11/2=110
c) SG (1+2+3+................+30)-(1+2+3+.........+10)=30*31/2-10*11/2=465-55=410
(5ⁿ)³x5²
5⁴¹⁰=(5ⁿ)³x5²
410=n³+2 n=∛408 dc.faci verificarea e ok!
d)SG 4(5+6+7+....+12)=4[(1+2+.......12)-(1+2+3+4)]=4[78-10]=4*68=272
7²⁷²=7²ⁿ 272=2n n=136
e) aflam nr.de termeni (75-5):7+1=11termeni
nu mi amintesc formula SG ptr. aceasta suma,mai caut si dc.gasesc termin ex.
f) SG (1+2+3+4+..........+49)-2(1+2+3+...........+24)=49*50/2-2*24*25/2=1225-600=625
13⁶²⁵=(13ⁿ)²⇒625=n²⇒n=25
